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Enter the market or not?

2013-01-10T23:36:18Z

Qantw00:

*'''Project name''': Enter the market or not?
*'''Class''': 4IT495 Simulation of Systems (WS 2012/2013)
*'''Author''': Wagon Antoine
*'''Model type''': Agent-based simulation
*'''Software used:''' NetLogo

=Problem definition=
This model aims to analyze the behavior of a monopoly company that is threatened by the entrance of a newcomer. Particularly, we can illustrate it with the fast-food situation in Belgium. For the purpose of this simulation, we will assume that McDonald’s is the only player on the market (in reality, there are of course other players like Quick or Hector Chicken). We will therefore analyze how McDonald’s behave when the Burger King firm tries to enter the market.

=Method=
Basically the Burger King chain will base its entry decision on a single fact. If there is only one firm, it wins that there is a market to share and will decide to build a fast food. Later, if McDonald decides to build another one, Burger King will assume that it exists more market to share and will therefore build a new one as well. Thus, Burger King acts here like a follower that copies the McDonald’s strategy. However, there will be a limitation in the model, resulting in a maximum number of companies.

Then, the McDonald’s fast food will decide if they fight or accommodate the nearest Burger King (direct concurrent). If they fight, they will either increase the quality or decrease the price. If the prices are too low or the quality too high, they can also decide to build a new restaurant in order to increase its market share.

Finally, the customers will have some preferences. Indeed here, the products are not homogeneous and people will have different tastes and preferences. Some will only consider the distance. Other will only go in their favorite fats food chain, no matter the distance. The last ones will consider the best price and quality in order to decide where they will eat.

To model this situation, I will use NetLogo. Indeed, here we have a situation with different agents interacting with each other. NetLogo will help us to have a good and powerful representation and visualization of the problem. NetLogo will allow us to monitor and analyze the results easier by changing the different variables. Here, NetLogo will display the different fast food restaurants, the customers and the link that exist between then (a link between a customer and a restaurant represents the fact that this customer will go there when he wants to eat in a fast food).

=Detailed description=

==Customers==

The first type of agent is the customer. A customer is defined by two main variables. First, they own a preference profile. Here, there are three main possibilities:

*No preference: in this case, the customer does not have any preference. To decide, he will only consider the distance and choose the nearest restaurant.
*Exclusive preference: Here, the customer will go in his favorite restaurant, no matter the distance.
*Relative preference: the last possibility is that the customer has no real preference. It this case, he will choose the fast food restaurant with the best quality. Of course, only the two nearest restaurants (one of each) will be analyzed.

When a customer agent is created, the preference is randomly set. Here, the weighting is set up arbitrarily: 30% of chance to get no preference; 30% of chance to get an exclusive preference; 40% of chance to get the relative preference.

The second variable will be the preference between the both companies if there is a preference. It is also set up randomly. Here, the variable is linked to a slider that will allow the tester to decide the probability to prefer one or another fast food chain.

At each tick, the customer will again decide where he wants to eat. Indeed, it is possible that he changes his mind. There are two different possibilities. First the customer can have no preference and a new fast food can be built closer to him. Second, he can have relative preference and another fast food with better quality or price can open close to him. In conclusion, we can analyze how customers will be assigned to one or another fast food and when they will change their mind.

==Fast foods==

'''McDonald’s'''

The first fast food agent that we will analyze is the monopoly (McDonald’s). The McDonald’s will be represented by four main variables. First, they will have a certain price and a certain quality (from 0 to 1). As it is a monopoly, we will set these two variables to 0 (0 being the biggest price or the lowest quality). In other words, the bigger the variable, the more customer-friendly it is. The third variable will be the fighting propensity that is a random number between 0 and 1. It means that the more the company is inclined to fight, the more it will use technics as increasing the quality or decreasing the price. It is set randomly. Moreover, the tester can decide the probability that is represented by the slider “fighting level”. The closer to 0 is the fighting level, the bigger the company will be inclined to fight. The last variable is the oldness and it will be used in order to recognize which business is old or not. Arbitrarily, we set the number of McDonald’s to 5 when we setup the model.

Basically, for each McDonald, we will look for the closest Burger King that will be the main competitor. When the closest Burger King is chosen, we will see if the McDonald fights or accommodate. Thus, if the fighting propensity is below the fighting level, they will accommodate. As a consequence, the McDonald will copy the Burger King strategy and set its price and quality to the exact same level. In the other case, if the fighting propensity is above the fighting level, we will play head or tails in order to see if they increase the quality or decrease the price. There is a last possibility. Sometimes, if the McDonald chain has improved too much its situation, they can decide to open a new restaurant. There is thus a condition: if the mean price and the mean quality are above a certain level (0.5 in the model), there is 20% of chance that they open a new restaurant (20% because it is still a big decision to open another restaurant). The last condition is that it does not go over the maximum amount of firms possible. At the beginning, it is set to 20 but the tester thanks to the input button can change it.

'''Burger King'''

The other fast food chain is Burger King and has fewer variables. They are only represented by a price and a quality and finally the oldness as the McDonald’s. Here the Burger King will decide to enter or not in the market. As explained above, the principle behind this is very simple. We just compute the number of McDonald’s and the number of Burger Kings. If there are more McDonald’s, a new Burger King will be built. Again, we cannot go over 20 firms in total on the market.

==Global variables==
In this model, there are four different global variables:

*Mean-price: it computes the mean price of the McDonald’s and is used for the decision to open a new fast food or not
*Mean-quality: idem
*Nbmc: it computes the number of McDonald’s and is used for several computations as explained above
*Nbbk: idem for the number of Burger Kings.

==Synthesis==
In conclusion, the following steps compose the model:

'''During the setup:'''
*Clear-all: clean all the model
*Reset-ticks: reset the model
*Setup-customers people: it creates the customers of the model (people is represented by the input button such that the tester can decide the number)
*Setup-mcdonalds 5: we first create 5 McDonald’s that act as a monopoly. We also set the price and the quality of all of them to 0.
*Associate-customers: here, we first associate each customer to the closest McDonald.

'''During the Go step:'''
*Set nbmc count mcdonalds: here, we define a variable that will compute the number of open McDonalds. It will be used for the entry game of Burger King
*Set nbbk count burgerkings: same as for McDonald’s
*Enter-or-not: it will decide as explained above if the Burger King chain opens a new restaurant or not
*Fight-accommodate: here, it is the process where the McDonald’s decides its strategy, depending on the fighting propensity and the fighting level.
*Customer-choice: the customer decides the fast food where he wants to eat

==Display==
The display of this model is quite simple. The customers have a “person” shape of a random color and are spread randomly over the plot. The fast foods have the “house” shape and are also built randomly. We can distinguish the both chains by the color: the McDonald’s will be yellow and the Burger Kings red. Finally, we can observe the choice of the customers by some links that are created during the “customer-choice” step. These links will have the color of the fast food.

=Results=

Here, we can analyze the results when we change the different variables.

==Number of customers==
The number of customers does not seem to affect the results. In general, the monopoly firm tends to remain the leader on the market. These results are confirmed when we increase the variable.

==Maximum number of firms==
As for the number of customers, this variable does not seem to affect the results and the monopoly firm remains the leader. Moreover, we can begin to observe a pattern. In most of the simulations, the challenger has more market share at the beginning but the leader takes back its position in the future. It can be explained in the code with the fight-accommodate step. Indeed, the McDonald’s restaurant will increase their service (quality or price). As a consequence, 40% of the customers on average will tend to go there, even if they were Burger King’s customers before and this because of the better service they offer by fighting the challenger.

==Favorite fast food==
To remind, the more the slider is on the left (close to 0), the bigger the probability to prefer the Burger King. Obviously here, when we will set the slider to the left, more people will prefer the challenger and it will provide mitigated results (more cases when the challenger has the biggest market share. When we approach and go over the 0.5 (50% of chance to prefer McDonald or Burger King), the previous pattern comes back and the monopoly remains the leader. Therefore in this model, the solution for the challenger would be to increase its service and to copy the leader.

==Fighting level==
As explained above, the fighting level will define the propensity of the McDonald’s to fight its competitors (i.e. increase quality or decrease price). The closer to 0, the more the leader will fight and gain market share. However, when we move the slider to the right, the challenger gains increasingly more market share because the leader copies him.

=Conclusion=
In conclusion, we can say that there is a pattern emerging from this model and saying that the position of the monopoly remains in general the best one. Indeed, in most of the simulations, at the end the McDonald’s company was in a better position with a bigger market share. The general pattern was the following: first, all the clients go to the leader that offers high price for bad quality. When the challenger arrives, he gets most of the market by improving the service. However, in the future, the leader fights and increases its service in order to beat its competitors. At this time, they get their market again and win in the end.

However, there are some limitations in this model:
*First, here the monopoly firm is the only one to change its attributes (price/quality) and to fight its competitors. Indeed, here when a Burger King restaurant opens, the quality and price are fixed randomly and then do not change anymore, what does not reflect the real world.
*Second, the model applies only one direct competitor. But this combination will not always be the two restaurants that are the closest to a customer. For example, if we had a fighting propensity equal to 1, it would mean that the leader completely accommodate and the result should be 50/50 regarding the market share, which is not the case. In conclusion, a McDonald will copy the price and quality of a Burger King but a customer will not base his decision on these both restaurants, what will false the results.
*The entry decision here is only based on a simple concept. This could be replaced with a more complex decision process, taking more variables into account. Moreover, here the restaurants are built on a random place, what does not reflect the real world. In real, restaurants would probably be near their competitors.

As a final conclusion, we can say that it is still better to have the monopoly role in this kind of games. Nevertheless, this model could be refined regarding to the limitations in order to provide a more powerful and complex simulation of the real world.

=Source code=

[[File:Enter_the_market_or_not?.nlogo.zip‎]]

Enter the market or not?

2013-01-10T23:33:51Z

Qantw00: /* Source code */

*'''Project name''': Enter the market or not?
*'''Class''': 4IT495 Simulation of Systems (SS 2012/2013)
*'''Author''': Wagon Antoine
*'''Model type''': Agent-based simulation
*'''Software used:''' NetLogo

=Problem definition=
This model aims to analyze the behavior of a monopoly company that is threatened by the entrance of a newcomer. Particularly, we can illustrate it with the fast-food situation in Belgium. For the purpose of this simulation, we will assume that McDonald’s is the only player on the market (in reality, there are of course other players like Quick or Hector Chicken). We will therefore analyze how McDonald’s behave when the Burger King firm tries to enter the market.

=Method=
Basically the Burger King chain will base its entry decision on a single fact. If there is only one firm, it wins that there is a market to share and will decide to build a fast food. Later, if McDonald decides to build another one, Burger King will assume that it exists more market to share and will therefore build a new one as well. Thus, Burger King acts here like a follower that copies the McDonald’s strategy. However, there will be a limitation in the model, resulting in a maximum number of companies.

Then, the McDonald’s fast food will decide if they fight or accommodate the nearest Burger King (direct concurrent). If they fight, they will either increase the quality or decrease the price. If the prices are too low or the quality too high, they can also decide to build a new restaurant in order to increase its market share.

Finally, the customers will have some preferences. Indeed here, the products are not homogeneous and people will have different tastes and preferences. Some will only consider the distance. Other will only go in their favorite fats food chain, no matter the distance. The last ones will consider the best price and quality in order to decide where they will eat.

To model this situation, I will use NetLogo. Indeed, here we have a situation with different agents interacting with each other. NetLogo will help us to have a good and powerful representation and visualization of the problem. NetLogo will allow us to monitor and analyze the results easier by changing the different variables. Here, NetLogo will display the different fast food restaurants, the customers and the link that exist between then (a link between a customer and a restaurant represents the fact that this customer will go there when he wants to eat in a fast food).

=Detailed description=

==Customers==

The first type of agent is the customer. A customer is defined by two main variables. First, they own a preference profile. Here, there are three main possibilities:

*No preference: in this case, the customer does not have any preference. To decide, he will only consider the distance and choose the nearest restaurant.
*Exclusive preference: Here, the customer will go in his favorite restaurant, no matter the distance.
*Relative preference: the last possibility is that the customer has no real preference. It this case, he will choose the fast food restaurant with the best quality. Of course, only the two nearest restaurants (one of each) will be analyzed.

When a customer agent is created, the preference is randomly set. Here, the weighting is set up arbitrarily: 30% of chance to get no preference; 30% of chance to get an exclusive preference; 40% of chance to get the relative preference.

The second variable will be the preference between the both companies if there is a preference. It is also set up randomly. Here, the variable is linked to a slider that will allow the tester to decide the probability to prefer one or another fast food chain.

At each tick, the customer will again decide where he wants to eat. Indeed, it is possible that he changes his mind. There are two different possibilities. First the customer can have no preference and a new fast food can be built closer to him. Second, he can have relative preference and another fast food with better quality or price can open close to him. In conclusion, we can analyze how customers will be assigned to one or another fast food and when they will change their mind.

==Fast foods==

'''McDonald’s'''

The first fast food agent that we will analyze is the monopoly (McDonald’s). The McDonald’s will be represented by four main variables. First, they will have a certain price and a certain quality (from 0 to 1). As it is a monopoly, we will set these two variables to 0 (0 being the biggest price or the lowest quality). In other words, the bigger the variable, the more customer-friendly it is. The third variable will be the fighting propensity that is a random number between 0 and 1. It means that the more the company is inclined to fight, the more it will use technics as increasing the quality or decreasing the price. It is set randomly. Moreover, the tester can decide the probability that is represented by the slider “fighting level”. The closer to 0 is the fighting level, the bigger the company will be inclined to fight. The last variable is the oldness and it will be used in order to recognize which business is old or not. Arbitrarily, we set the number of McDonald’s to 5 when we setup the model.

Basically, for each McDonald, we will look for the closest Burger King that will be the main competitor. When the closest Burger King is chosen, we will see if the McDonald fights or accommodate. Thus, if the fighting propensity is below the fighting level, they will accommodate. As a consequence, the McDonald will copy the Burger King strategy and set its price and quality to the exact same level. In the other case, if the fighting propensity is above the fighting level, we will play head or tails in order to see if they increase the quality or decrease the price. There is a last possibility. Sometimes, if the McDonald chain has improved too much its situation, they can decide to open a new restaurant. There is thus a condition: if the mean price and the mean quality are above a certain level (0.5 in the model), there is 20% of chance that they open a new restaurant (20% because it is still a big decision to open another restaurant). The last condition is that it does not go over the maximum amount of firms possible. At the beginning, it is set to 20 but the tester thanks to the input button can change it.

'''Burger King'''

The other fast food chain is Burger King and has fewer variables. They are only represented by a price and a quality and finally the oldness as the McDonald’s. Here the Burger King will decide to enter or not in the market. As explained above, the principle behind this is very simple. We just compute the number of McDonald’s and the number of Burger Kings. If there are more McDonald’s, a new Burger King will be built. Again, we cannot go over 20 firms in total on the market.

==Global variables==
In this model, there are four different global variables:

*Mean-price: it computes the mean price of the McDonald’s and is used for the decision to open a new fast food or not
*Mean-quality: idem
*Nbmc: it computes the number of McDonald’s and is used for several computations as explained above
*Nbbk: idem for the number of Burger Kings.

==Synthesis==
In conclusion, the following steps compose the model:

'''During the setup:'''
*Clear-all: clean all the model
*Reset-ticks: reset the model
*Setup-customers people: it creates the customers of the model (people is represented by the input button such that the tester can decide the number)
*Setup-mcdonalds 5: we first create 5 McDonald’s that act as a monopoly. We also set the price and the quality of all of them to 0.
*Associate-customers: here, we first associate each customer to the closest McDonald.

'''During the Go step:'''
*Set nbmc count mcdonalds: here, we define a variable that will compute the number of open McDonalds. It will be used for the entry game of Burger King
*Set nbbk count burgerkings: same as for McDonald’s
*Enter-or-not: it will decide as explained above if the Burger King chain opens a new restaurant or not
*Fight-accommodate: here, it is the process where the McDonald’s decides its strategy, depending on the fighting propensity and the fighting level.
*Customer-choice: the customer decides the fast food where he wants to eat

==Display==
The display of this model is quite simple. The customers have a “person” shape of a random color and are spread randomly over the plot. The fast foods have the “house” shape and are also built randomly. We can distinguish the both chains by the color: the McDonald’s will be yellow and the Burger Kings red. Finally, we can observe the choice of the customers by some links that are created during the “customer-choice” step. These links will have the color of the fast food.

=Results=

Here, we can analyze the results when we change the different variables.

==Number of customers==
The number of customers does not seem to affect the results. In general, the monopoly firm tends to remain the leader on the market. These results are confirmed when we increase the variable.

==Maximum number of firms==
As for the number of customers, this variable does not seem to affect the results and the monopoly firm remains the leader. Moreover, we can begin to observe a pattern. In most of the simulations, the challenger has more market share at the beginning but the leader takes back its position in the future. It can be explained in the code with the fight-accommodate step. Indeed, the McDonald’s restaurant will increase their service (quality or price). As a consequence, 40% of the customers on average will tend to go there, even if they were Burger King’s customers before and this because of the better service they offer by fighting the challenger.

==Favorite fast food==
To remind, the more the slider is on the left (close to 0), the bigger the probability to prefer the Burger King. Obviously here, when we will set the slider to the left, more people will prefer the challenger and it will provide mitigated results (more cases when the challenger has the biggest market share. When we approach and go over the 0.5 (50% of chance to prefer McDonald or Burger King), the previous pattern comes back and the monopoly remains the leader. Therefore in this model, the solution for the challenger would be to increase its service and to copy the leader.

==Fighting level==
As explained above, the fighting level will define the propensity of the McDonald’s to fight its competitors (i.e. increase quality or decrease price). The closer to 0, the more the leader will fight and gain market share. However, when we move the slider to the right, the challenger gains increasingly more market share because the leader copies him.

=Conclusion=
In conclusion, we can say that there is a pattern emerging from this model and saying that the position of the monopoly remains in general the best one. Indeed, in most of the simulations, at the end the McDonald’s company was in a better position with a bigger market share. The general pattern was the following: first, all the clients go to the leader that offers high price for bad quality. When the challenger arrives, he gets most of the market by improving the service. However, in the future, the leader fights and increases its service in order to beat its competitors. At this time, they get their market again and win in the end.

However, there are some limitations in this model:
*First, here the monopoly firm is the only one to change its attributes (price/quality) and to fight its competitors. Indeed, here when a Burger King restaurant opens, the quality and price are fixed randomly and then do not change anymore, what does not reflect the real world.
*Second, the model applies only one direct competitor. But this combination will not always be the two restaurants that are the closest to a customer. For example, if we had a fighting propensity equal to 1, it would mean that the leader completely accommodate and the result should be 50/50 regarding the market share, which is not the case. In conclusion, a McDonald will copy the price and quality of a Burger King but a customer will not base his decision on these both restaurants, what will false the results.
*The entry decision here is only based on a simple concept. This could be replaced with a more complex decision process, taking more variables into account. Moreover, here the restaurants are built on a random place, what does not reflect the real world. In real, restaurants would probably be near their competitors.

As a final conclusion, we can say that it is still better to have the monopoly role in this kind of games. Nevertheless, this model could be refined regarding to the limitations in order to provide a more powerful and complex simulation of the real world.

=Source code=

[[File:Enter_the_market_or_not?.nlogo.zip‎]]

File:Enter the market or not?.nlogo.zip

2013-01-10T23:31:47Z

Qantw00:

Enter the market or not?

2013-01-10T23:30:24Z

Qantw00: Created page with "*'''Project name''': Enter the market or not? *'''Class''': 4IT495 Simulation of Systems (SS 2012/2013) *'''Author''': Wagon Antoine *'''Model type''': Agent-based simulation ..."

Simulations

2013-01-10T23:19:54Z

Qantw00: /* Simulations WS 2012/2013 */

You can find hints for your simulation in [[How to deal with the simulation assignment]] article.

=Simulations WS 2012/2013=

Please, place here your [[Assignments WS 2012/2013|assignment proposals]].

* Jiří Hradil, xhraj18, [[A local restaurant during lunchtime]]
* Wagon Antoine, qantw00, [[Enter the market or not?]]

=Simulations SS 2011/2012=
* Khabirova Maja, xkham00 - [[Simulation of a parking lot in Saint-Petersburg Airport|Simulation of a parking lot in Saint-Petersburg Airport]]

Extensive form

2013-01-06T12:19:30Z

Qantw00:

__TOC__
==Introduction==
The normal form games give a representation of players that make decisions simultaneously. However, in these games, players do not have any information about the other players’ strategies when they make their own choice. However, in lots of different situations, players make their decisions depending of the past choices of other players (e.g. chess game, auctions, negotiation, etc.). To represent this kind of games, we can use the extensive form by implementing game trees. In this paper, we will first define the concept of extensive form game. After illustrating it with some concrete examples, we will describe the typology and the different variants that can exist in this kind of games. Fourth, we will analyze more in detail the notion of strategy. Finally, we will study how we can solve this kind of games by introducing the concept of backward induction.

==Definition==
An extensive form game will be composed by several main components:
*Players: more often we consider games with two players.
*Procedure: who moves when and what are the possible choices are questions that have to be defined in the game.
*Information: it is important to know if we are in a situation with perfect and complete information or not.
*History: is the sequence of actions taken by the players up to some decision point. A terminal history is a history that contains the action choices of all the players up until the point where the payoff is distributed.
*Payoffs: finally, it is crucial to determine the different payoffs in function of the decisions made.

Here, we use the game trees in order to represent the extensive form games. The decisions are made at the nodes included in the set X. There is also an initial node at which the game begins. Then, the game evolves from node to node depending on the players’ decisions. The game ends when a terminal node is reached (set Z). At this point, players receive a payoff corresponding to the terminal node. The preferences of players (i = 1…I) are represented by utility functions ui. When a player has to decide, he might not know exactly at which of the nodes it’s located. There are thus information sets (set of nodes that all belong to the same player and at all of which the same set of action is available). We can thus observe that this kind of games can be divided into smaller sub-games that represent sub-trees according to the different information sets.

Now that the background is set, let us express the extensive form games in a formal notation. Here, the methodology of Levin (2002) will be used:
*A set of players i = 1, …, I
*A finite set X of nodes that form the game tree, with Z ⊂ X being the terminal nodes.
*A set of functions that describe for each x ∉ Z,
:The player i(x) who moves at x.
:The set A(x) of possible actions at x.
:The successor node n(x, a) resulting from action a.
*Payoff functions ui : Z → ℜ assigning payoffs to players as a function of the terminal node reached.
*An information partition: for each x, let h(x) denote the set of nodes that are possible given what player i(x) knows. Thus, if x′ ∈ h(x), then i(x′) = i(x), A(x′) = A(x) and h(x′) = h(x).
We can also use the notation i(h) or A(h) to denote the player who moves at information set h and his set of possible actions.

==Concrete examples==

===Entry game===
There is a firm M that has a monopoly on the market. Another firm E can decide to enter or not this market. If the firm E decides to enter the market, the monopoly firm can decide either to fight or to accommodate. The payoffs are the following: (2,0) if E does not enter; (-1, -1) if E enters and M fights and finally (1, 1) if E enters and M accommodates. The following game tree can represent it:

<center>[[File:extensive1.png]]</center>

===Matching pennies===
We can also consider the matching pennies game. Here, the first player either chooses head or tail. The second player then also chooses head or tail. If both pennies have the same face, the second player wins; if not, the player 1 wins. A variant of this game can be that both players choose at the same time. The second player thus chooses without knowing the result of the first player (it is represented on the second graph). It is important to notice that the resulting payoffs are the same in both cases.

<center>[[File:extensive2.png]]</center>

==Typology==

===Perfect and complete information===
It exists different types of extensive form games. Indeed, in some games, all the players know exactly each move of the others. The information is thus perfect and they can base their decision on the past moves of others. Moreover, if every player is aware of the entire tree (nothing is hidden or related to the chance), the game will be complete. For example, the chess game is perfect and complete. Indeed, each player knows the moves of the opponent and everyone knows all the possible moves they can achieve. It is also the case of the entry game explained above. In conclusion, all the information sets here is a singleton.

===Imperfect information===
Sometimes, it happens that one or several players do not get the perfect information. Indeed, it is possible that when a player has to decide, he does not know the past decision of the other player. In other words, a player sometimes cannot observe the choice of another player. Therefore, it means that moves can be simultaneous or a move could be hidden. The information set here will not be a singleton anymore. Graphically, it is represented by a dotted line connecting all the nodes of the information set (as on the tree of the variant of the matching pennies game). In conclusion, if a game is composed from at least one information set with more than one node, the game has imperfect information.

===Incomplete information===
In some games, it is also possible that some information is missing. For example, it is possible that a player does not know all the payoffs of the game. Some other information can also be missing: available nodes or decisions, the type or number of other players, the decision order, etc. In order to determine the type of the players, a so-called “nature” can be used (represented by a non-filled node) using a probability distribution. Here, each player observes his type but the other players do not. In conclusion, as we know that the payoff of the terminal node depends of the type of the player, nobody is sure about the payoff matrix. The game has thus incomplete information. An example of this is the auction game.

===Finite or infinite games===
A last typology can distinguish finite and infinite games. In the first case, there is a finite set of actions at each decision node. In the latter case, it can arise that at a decision node, there is an infinite number of possible actions. For example, if we have a Stackelberg competition, we can imagine that the decision node will be to define the quantity to produce. However, these quantities can take infinite value.

==Strategies==
A strategy is a complete contingent plan explaining what a player will do in every situation. Thus, for all the information sets, we can express the strategies as the different possible decision that the player can make.

===Pure strategy===
If we continue with the formal notation, we can define a pure strategy for a player i as a function si: Hi → Ai such that si(h) ∈ A(h) for each h ∈ Hi.
Let Si denote the set of pure strategies available to player i, and S = S1 × ... × SI denote the set of pure strategy profiles. As before, we will let s = (s1, ..., sI ) denote a strategy profile, and s−i the strategies of i’s opponents. For example, if we take the entry game, here are the strategies of both players:
:S1=[out-fight; out-accommodate; in-fight; in-accommodate]
:S2=[in-out]<br>
We can notice here that if we make a list of all players and their pure strategies, we can represent the extensive form game with its associated normal form.

===Mixed strategy===
A mixed strategy for player i in an extensive form game is a probability distribution over pure strategies, i.e. some σi ∈ ∆(Si).
In a mixed strategy, the player randomly chooses at the beginning a pure strategy that he will use afterwards. When this strategy is chosen, he continues by following this deterministic rule of decisions.

===Behavioural strategy===
A behavioural strategy for player i in an extensive form game is a function σi : Hi → ∆(Ai) such that support(σi(h)) ⊂ A(h) for all h ∈ Hi.
On the opposite, a behavioural strategy can be seen as stochastic. Indeed, here a random decision will be made at each decision node. Here, the hazard is focused on the next action and not on a global rule of behaviour as for mixed strategy.

There is a theorem linking these two types of strategies: the Kuhn’s Theorem. It says that if we have a game with perfect recall (i.e. players always remember past decision and information they had while making those decisions), mixed and behavioural strategies are equivalent. It means that there is an equivalent behavioural strategy for any mixed strategy.

==Strategic form of extensive form games==
In order to solve extensive form games, we can also use the concept of Nash equilibrium of the normal form, as explained above. We will also show in the next sections that it allows providing more detailed predictions (e.g. sub-game perfect equilibrium). Let us take again the entry game example. Gathering all the strategies, we can build the associated normal form as follow:

<center>
{| border="1"
|
|'''Allow'''
|'''Fight'''
|-
|'''In'''
|align="center"|(2,1)
|align="center"|(0,0)
|-
|'''Out'''
|align="center"|(1,2)
|align="center"|(1,2)
|}
</center>

Therefore, now that we transformed the extensive form game, we can analyse it and see that there are two pure Nash equilibria (Challenge-Accommodate and Stay out-Fight). However, this is not completely right. Indeed, using the normal form, the Nash equilibria do not take into account the sequential structure of that game. It treats strategies as choices that are decided in one time and forever. Thus, we need an equilibrium that gives optimal strategies for all players not only at start but also at every moment of history. To do this, we first need to define the concept of sub-game.

==Sub-game==
A sub-game is a part of the game that can be seen as a game itself. It owns a single initial node and includes all the successive nodes starting from there. In other words, when the initial node of a sub-game is reached, players can focus only on it and forget the past history of the game. Again, we can give the formal notation of a sub-game:
Let G be an extensive form game, a sub-game G′ of G consists of (i) a subset Y of the nodes X consisting of a single non-terminal node x and all of its successors, which has the property that if y ∈ Y, y′ ∈ h(y) then y′ ∈ Y , and (ii) information sets, feasible moves, and payoffs at terminal nodes as in G.
Let us illustrate it with an example:

<center>[[File:extensive3.png]]</center>

Here we can see that there are five different sub-games. First, there is the game itself (G). Second, we have a sub-game starting when C is selected at the first step (G4). Then, we have two different sub-games, depending of the decision of player 1 (G2 and G3). Finally, we have a last sub-game that includes the last decision of player 2. Doing this, we can refine the model and analyse if there is any sub-game perfect equilibrium. We can define a sub-game perfect equilibrium as follow (Selten, 1965): A sub-game perfect Nash equilibrium (SPNE) is a profile of strategies such that in each sub-game the induced strategy profile is a Nash equilibrium of that sub-game. Moreover, we can add that in every extensive form game there is at least one sub-game perfect equilibrium. Now we are therefore able to refine the Nash equilibria in order to define the more precise equilibria. To achieve this, we can use the backward induction methodology, describe in the following section.

==Backward induction==
Basically, the backward induction process is an iterative method in order to find the optimal strategies and Nash equilibria in extensive form or sequential games. The principle is quite simple: we first start by defining the optimal strategy of the player that makes the last move. Regarding this decision, we analyse the optimal strategy for the player that makes the previous move. In other words, what would he do knowing the optimal strategy of the other player. Finally, we continue this process till we reach the initial node. Doing this, we can determine the Nash equilibria of each sub-game of the original game. At the end, we will be able to define the sub-game perfect equilibrium.

Let us illustrate this with a new example. Consider the following game:

<center>[[File:extensive4.png]]</center>

In this extensive form game, the first player chooses one action (C or D). Depending of this, the second player chooses his final action (E or F). The different payoffs are at the bottom of the graph. Here, we can see that we have three sub-games (the game itself and the two sub-games, depending on the player 1’s decision.

<center>[[File:extensive5.png]]</center>

We start by analysing the two different sub-games. In the first one, if player 1 chooses action C, the second player will automatically choose the action E because it gives a better payoff (1 > 0). In the other sub-game on the opposite, if player 1 chooses D, the player 2 will choose action F for the same reason as the previously (3 > 2). Now that we have the optimal strategies for the last move, we can go upstream in order to find the optimal strategy of player 1. To do this, we compare his payoff in both situations. If he chooses the action C, the player 1 will get a utility of 2. In the other case, he will receive only 1. Player 1 will thus decide to take the action C because he knows that doing this, the second player will choose E and then he will get a better payoff. The strategy (C-E) is therefore the sub-game perfect equilibrium. In this case, it is the only sub-game perfect equilibrium.
However the backward induction cannot be applied to every extensive form games. Indeed, sometimes if the game is infinitely long, it will be impossible to determine the sub-game perfect equilibria. However, it is possible to apply this methodology even if we have an imperfect information game.

==Chance moves==
A last concept that is important to stress out is that sometimes it is possible that chance nodes appear in the extensive form game. Indeed, depending on a choice, it is possible to reach different path according to a probability function.

<center>[[File:extensive6.png]]</center>

We can observe in this game that if the first player chooses the action B, we reach the chance node. There is 50% of chance that the game stops with a certain payoff (3,0) and 50% of chance that the second player has to make a final decision. Here, we can also apply the backward induction to find the sub-game perfect equilibrium. Let us start with the final sub-game. The second player will automatically choose action C because it gives a better payoff. Knowing this, the first player has two possibilities. First, he can choose action A and the game end with the payoff (1,1). Second, he can decide to go on the chance node. In this case, he has 50% chance to get a utility of 3 but 50% chance to receive nothing. The total utility is thus 50% of 3 + 50% of 0 = 1,5. This payoff is better than 1 if he chooses action A and will thus decide to take action B. The perfect equilibrium here is thus (A-C).

==Exercises==
:'''1. Consider the following extensive form game:'''

<center>[[File:extensive7.png]]</center>

:a) Find all the Nash equilibria of the game
:b) Find all the sub-game perfect equilibria of the game

:'''2. In an extensive form game two nodes are in the same information set whenever'''

:(a) They belong to different players and players cannot differentiate between them.
:(b) They belong to the same player and that player cannot differentiate be- tween them.
:(c) They belong to different players and players can differentiate between them.
:(d) They belong to the same player and that player can differentiate between them.
:(e) None of the above.

:'''3. If we solve the following game with backwards induction, what is the resulting payoff?'''

<center>[[File:extensive8.png]]</center>

==References==
*Lenaerts, T. (2012). Learning Dynamics, seen on http://ai.vub.ac.be/sites/default/files/Extensive%20form.pdf the 5th of January
*Levin, J. (2002). Extensive form games, seen on http://www.stanford.edu/~jdlevin/Econ%20203/ExtensiveForm.pdf the 4th of January
*Ratliff, J. (1997). Strategies in Extensive-Form Games, seen on http://www.virtualperfection.com/gametheory/4.2.StrategiesInExtensiveFormGames.1.0.pdf the 4th of January
*Von Stengel, B., Van Den Elzen, A., Talman D. (2002). Computing normal form perfect equilibria for extensive two-person games, Econometrica, Vol. 70, No. 2 (March), pp.693-715

Extensive form

2013-01-06T12:17:34Z

Qantw00:

__TOC__
==Introduction==
The normal form games give a representation of players that make decisions simultaneously. However, in these games, players do not have any information about the other players’ strategies when they make their own choice. However, in lots of different situations, players make their decisions depending of the past choices of other players (e.g. chess game, auctions, negotiation, etc.). To represent this kind of games, we can use the extensive form by implementing game trees. In this paper, we will first define the concept of extensive form game. After illustrating it with some concrete examples, we will describe the typology and the different variants that can exist in this kind of games. Fourth, we will analyze more in detail the notion of strategy. Finally, we will study how we can solve this kind of games by introducing the concept of backward induction.

==Definition==
An extensive form game will be composed by several main components:
*Players: more often we consider games with two players.
*Procedure: who moves when and what are the possible choices are questions that have to be defined in the game.
*Information: it is important to know if we are in a situation with perfect and complete information or not.
*History: is the sequence of actions taken by the players up to some decision point. A terminal history is a history that contains the action choices of all the players up until the point where the payoff is distributed.
*Payoffs: finally, it is crucial to determine the different payoffs in function of the decisions made.

Here, we use the game trees in order to represent the extensive form games. The decisions are made at the nodes included in the set X. There is also an initial node at which the game begins. Then, the game evolves from node to node depending on the players’ decisions. The game ends when a terminal node is reached (set Z). At this point, players receive a payoff corresponding to the terminal node. The preferences of players (i = 1…I) are represented by utility functions ui. When a player has to decide, he might not know exactly at which of the nodes it’s located. There are thus information sets (set of nodes that all belong to the same player and at all of which the same set of action is available). We can thus observe that this kind of games can be divided into smaller sub-games that represent sub-trees according to the different information sets.

Now that the background is set, let us express the extensive form games in a formal notation. Here, the methodology of Levin (2002) will be used:
*A set of players i = 1, …, I
*A finite set X of nodes that form the game tree, with Z ⊂ X being the terminal nodes.
*A set of functions that describe for each x ∉ Z,
:The player i(x) who moves at x.
:The set A(x) of possible actions at x.
:The successor node n(x, a) resulting from action a.
*Payoff functions ui : Z → ℜ assigning payoffs to players as a function of the terminal node reached.
*An information partition: for each x, let h(x) denote the set of nodes that are possible given what player i(x) knows. Thus, if x′ ∈ h(x), then i(x′) = i(x), A(x′) = A(x) and h(x′) = h(x).
We can also use the notation i(h) or A(h) to denote the player who moves at information set h and his set of possible actions.

==Concrete examples==

===Entry game===
There is a firm M that has a monopoly on the market. Another firm E can decide to enter or not this market. If the firm E decides to enter the market, the monopoly firm can decide either to fight or to accommodate. The payoffs are the following: (2,0) if E does not enter; (-1, -1) if E enters and M fights and finally (1, 1) if E enters and M accommodates. The following game tree can represent it:

<center>[[File:extensive1.png]]</center>

===Matching pennies===
We can also consider the matching pennies game. Here, the first player either chooses head or tail. The second player then also chooses head or tail. If both pennies have the same face, the second player wins; if not, the player 1 wins. A variant of this game can be that both players choose at the same time. The second player thus chooses without knowing the result of the first player (it is represented on the second graph). It is important to notice that the resulting payoffs are the same in both cases.

<center>[[File:extensive2.png]]</center>

==Typology==

===Perfect and complete information===
It exists different types of extensive form games. Indeed, in some games, all the players know exactly each move of the others. The information is thus perfect and they can base their decision on the past moves of others. Moreover, if every player is aware of the entire tree (nothing is hidden or related to the chance), the game will be complete. For example, the chess game is perfect and complete. Indeed, each player knows the moves of the opponent and everyone knows all the possible moves they can achieve. It is also the case of the entry game explained above. In conclusion, all the information sets here is a singleton.

===Imperfect information===
Sometimes, it happens that one or several players do not get the perfect information. Indeed, it is possible that when a player has to decide, he does not know the past decision of the other player. In other words, a player sometimes cannot observe the choice of another player. Therefore, it means that moves can be simultaneous or a move could be hidden. The information set here will not be a singleton anymore. Graphically, it is represented by a dotted line connecting all the nodes of the information set (as on the tree of the variant of the matching pennies game). In conclusion, if a game is composed from at least one information set with more than one node, the game has imperfect information.

===Incomplete information===
In some games, it is also possible that some information is missing. For example, it is possible that a player does not know all the payoffs of the game. Some other information can also be missing: available nodes or decisions, the type or number of other players, the decision order, etc. In order to determine the type of the players, a so-called “nature” can be used (represented by a non-filled node) using a probability distribution. Here, each player observes his type but the other players do not. In conclusion, as we know that the payoff of the terminal node depends of the type of the player, nobody is sure about the payoff matrix. The game has thus incomplete information. An example of this is the auction game.

===Finite or infinite games===
A last typology can distinguish finite and infinite games. In the first case, there is a finite set of actions at each decision node. In the latter case, it can arise that at a decision node, there is an infinite number of possible actions. For example, if we have a Stackelberg competition, we can imagine that the decision node will be to define the quantity to produce. However, these quantities can take infinite value.

==Strategies==
A strategy is a complete contingent plan explaining what a player will do in every situation. Thus, for all the information sets, we can express the strategies as the different possible decision that the player can make.

===Pure strategy===
If we continue with the formal notation, we can define a pure strategy for a player i as a function si: Hi → Ai such that si(h) ∈ A(h) for each h ∈ Hi.
Let Si denote the set of pure strategies available to player i, and S = S1 × ... × SI denote the set of pure strategy profiles. As before, we will let s = (s1, ..., sI ) denote a strategy profile, and s−i the strategies of i’s opponents. For example, if we take the entry game, here are the strategies of both players:
S1=[out-fight; out-accommodate; in-fight; in-accommodate]
S2=[in-out]
We can notice here that if we make a list of all players and their pure strategies, we can represent the extensive form game with its associated normal form.

===Mixed strategy===
A mixed strategy for player i in an extensive form game is a probability distribution over pure strategies, i.e. some σi ∈ ∆(Si).
In a mixed strategy, the player randomly chooses at the beginning a pure strategy that he will use afterwards. When this strategy is chosen, he continues by following this deterministic rule of decisions.

===Behavioural strategy===
A behavioural strategy for player i in an extensive form game is a function σi : Hi → ∆(Ai) such that support(σi(h)) ⊂ A(h) for all h ∈ Hi.
On the opposite, a behavioural strategy can be seen as stochastic. Indeed, here a random decision will be made at each decision node. Here, the hazard is focused on the next action and not on a global rule of behaviour as for mixed strategy.

There is a theorem linking these two types of strategies: the Kuhn’s Theorem. It says that if we have a game with perfect recall (i.e. players always remember past decision and information they had while making those decisions), mixed and behavioural strategies are equivalent. It means that there is an equivalent behavioural strategy for any mixed strategy.

==Strategic form of extensive form games==
In order to solve extensive form games, we can also use the concept of Nash equilibrium of the normal form, as explained above. We will also show in the next sections that it allows providing more detailed predictions (e.g. sub-game perfect equilibrium). Let us take again the entry game example. Gathering all the strategies, we can build the associated normal form as follow:

<center>
{| border="1"
|
|'''Allow'''
|'''Fight'''
|-
|'''In'''
|align="center"|(2,1)
|align="center"|(0,0)
|-
|'''Out'''
|align="center"|(1,2)
|align="center"|(1,2)
|}
</center>

Therefore, now that we transformed the extensive form game, we can analyse it and see that there are two pure Nash equilibria (Challenge-Accommodate and Stay out-Fight). However, this is not completely right. Indeed, using the normal form, the Nash equilibria do not take into account the sequential structure of that game. It treats strategies as choices that are decided in one time and forever. Thus, we need an equilibrium that gives optimal strategies for all players not only at start but also at every moment of history. To do this, we first need to define the concept of sub-game.

==Sub-game==
A sub-game is a part of the game that can be seen as a game itself. It owns a single initial node and includes all the successive nodes starting from there. In other words, when the initial node of a sub-game is reached, players can focus only on it and forget the past history of the game. Again, we can give the formal notation of a sub-game:
Let G be an extensive form game, a sub-game G′ of G consists of (i) a subset Y of the nodes X consisting of a single non-terminal node x and all of its successors, which has the property that if y ∈ Y, y′ ∈ h(y) then y′ ∈ Y , and (ii) information sets, feasible moves, and payoffs at terminal nodes as in G.
Let us illustrate it with an example:

<center>[[File:extensive3.png]]</center>

Here we can see that there are five different sub-games. First, there is the game itself (G). Second, we have a sub-game starting when C is selected at the first step (G4). Then, we have two different sub-games, depending of the decision of player 1 (G2 and G3). Finally, we have a last sub-game that includes the last decision of player 2. Doing this, we can refine the model and analyse if there is any sub-game perfect equilibrium. We can define a sub-game perfect equilibrium as follow (Selten, 1965): A sub-game perfect Nash equilibrium (SPNE) is a profile of strategies such that in each sub-game the induced strategy profile is a Nash equilibrium of that sub-game. Moreover, we can add that in every extensive form game there is at least one sub-game perfect equilibrium. Now we are therefore able to refine the Nash equilibria in order to define the more precise equilibria. To achieve this, we can use the backward induction methodology, describe in the following section.

==Backward induction==
Basically, the backward induction process is an iterative method in order to find the optimal strategies and Nash equilibria in extensive form or sequential games. The principle is quite simple: we first start by defining the optimal strategy of the player that makes the last move. Regarding this decision, we analyse the optimal strategy for the player that makes the previous move. In other words, what would he do knowing the optimal strategy of the other player. Finally, we continue this process till we reach the initial node. Doing this, we can determine the Nash equilibria of each sub-game of the original game. At the end, we will be able to define the sub-game perfect equilibrium.

Let us illustrate this with a new example. Consider the following game:

<center>[[File:extensive4.png]]</center>

In this extensive form game, the first player chooses one action (C or D). Depending of this, the second player chooses his final action (E or F). The different payoffs are at the bottom of the graph. Here, we can see that we have three sub-games (the game itself and the two sub-games, depending on the player 1’s decision.

<center>[[File:extensive5.png]]</center>

We start by analysing the two different sub-games. In the first one, if player 1 chooses action C, the second player will automatically choose the action E because it gives a better payoff (1 > 0). In the other sub-game on the opposite, if player 1 chooses D, the player 2 will choose action F for the same reason as the previously (3 > 2). Now that we have the optimal strategies for the last move, we can go upstream in order to find the optimal strategy of player 1. To do this, we compare his payoff in both situations. If he chooses the action C, the player 1 will get a utility of 2. In the other case, he will receive only 1. Player 1 will thus decide to take the action C because he knows that doing this, the second player will choose E and then he will get a better payoff. The strategy (C-E) is therefore the sub-game perfect equilibrium. In this case, it is the only sub-game perfect equilibrium.
However the backward induction cannot be applied to every extensive form games. Indeed, sometimes if the game is infinitely long, it will be impossible to determine the sub-game perfect equilibria. However, it is possible to apply this methodology even if we have an imperfect information game.

==Chance moves==
A last concept that is important to stress out is that sometimes it is possible that chance nodes appear in the extensive form game. Indeed, depending on a choice, it is possible to reach different path according to a probability function.

<center>[[File:extensive6.png]]</center>

We can observe in this game that if the first player chooses the action B, we reach the chance node. There is 50% of chance that the game stops with a certain payoff (3,0) and 50% of chance that the second player has to make a final decision. Here, we can also apply the backward induction to find the sub-game perfect equilibrium. Let us start with the final sub-game. The second player will automatically choose action C because it gives a better payoff. Knowing this, the first player has two possibilities. First, he can choose action A and the game end with the payoff (1,1). Second, he can decide to go on the chance node. In this case, he has 50% chance to get a utility of 3 but 50% chance to receive nothing. The total utility is thus 50% of 3 + 50% of 0 = 1,5. This payoff is better than 1 if he chooses action A and will thus decide to take action B. The perfect equilibrium here is thus (A-C).

==Exercises==
:'''1. Consider the following extensive form game:'''

<center>[[File:extensive7.png]]</center>

:a) Find all the Nash equilibria of the game
:b) Find all the sub-game perfect equilibria of the game

:'''2. In an extensive form game two nodes are in the same information set whenever'''

:(a) They belong to different players and players cannot differentiate between them.
:(b) They belong to the same player and that player cannot differentiate be- tween them.
:(c) They belong to different players and players can differentiate between them.
:(d) They belong to the same player and that player can differentiate between them.
:(e) None of the above.

:'''3. If we solve the following game with backwards induction, what is the resulting payoff?'''

<center>[[File:extensive8.png]]</center>

==References==
*Lenaerts, T. (2012). Learning Dynamics, seen on http://ai.vub.ac.be/sites/default/files/Extensive%20form.pdf the 5th of January
*Levin, J. (2002). Extensive form games, seen on http://www.stanford.edu/~jdlevin/Econ%20203/ExtensiveForm.pdf the 4th of January
*Ratliff, J. (1997). Strategies in Extensive-Form Games, seen on http://www.virtualperfection.com/gametheory/4.2.StrategiesInExtensiveFormGames.1.0.pdf the 4th of January
*Von Stengel, B., Van Den Elzen, A., Talman D. (2002). Computing normal form perfect equilibria for extensive two-person games, Econometrica, Vol. 70, No. 2 (March), pp.693-715

Extensive form

2013-01-06T12:06:17Z

Qantw00:

__TOC__
==Introduction==
The normal form games give a representation of players that make decisions simultaneously. However, in these games, players do not have any information about the other players’ strategies when they make their own choice. However, in lots of different situations, players make their decisions depending of the past choices of other players (e.g. chess game, auctions, negotiation, etc.). To represent this kind of games, we can use the extensive form by implementing game trees. In this paper, we will first define the concept of extensive form game. After illustrating it with some concrete examples, we will describe the typology and the different variants that can exist in this kind of games. Fourth, we will analyze more in detail the notion of strategy. Finally, we will study how we can solve this kind of games by introducing the concept of backward induction.

==Definition==
An extensive form game will be composed by several main components:
*Players: more often we consider games with two players.
*Procedure: who moves when and what are the possible choices are questions that have to be defined in the game.
*Information: it is important to know if we are in a situation with perfect and complete information or not.
*History: is the sequence of actions taken by the players up to some decision point. A terminal history is a history that contains the action choices of all the players up until the point where the payoff is distributed.
*Payoffs: finally, it is crucial to determine the different payoffs in function of the decisions made.

Here, we use the game trees in order to represent the extensive form games. The decisions are made at the nodes included in the set X. There is also an initial node at which the game begins. Then, the game evolves from node to node depending on the players’ decisions. The game ends when a terminal node is reached (set Z). At this point, players receive a payoff corresponding to the terminal node. The preferences of players (i = 1…I) are represented by utility functions ui. When a player has to decide, he might not know exactly at which of the nodes it’s located. There are thus information sets (set of nodes that all belong to the same player and at all of which the same set of action is available). We can thus observe that this kind of games can be divided into smaller sub-games that represent sub-trees according to the different information sets.

Now that the background is set, let us express the extensive form games in a formal notation. Here, the methodology of Levin (2002) will be used:
*A set of players i = 1, …, I
*A finite set X of nodes that form the game tree, with Z ⊂ X being the terminal nodes.
*A set of functions that describe for each x ∉ Z,
:The player i(x) who moves at x.
:The set A(x) of possible actions at x.
:The successor node n(x, a) resulting from action a.
*Payoff functions ui : Z → ℜ assigning payoffs to players as a function of the terminal node reached.
*An information partition: for each x, let h(x) denote the set of nodes that are possible given what player i(x) knows. Thus, if x′ ∈ h(x), then i(x′) = i(x), A(x′) = A(x) and h(x′) = h(x).
We can also use the notation i(h) or A(h) to denote the player who moves at information set h and his set of possible actions.

==Concrete examples==

===Entry game===
There is a firm M that has a monopoly on the market. Another firm E can decide to enter or not this market. If the firm E decides to enter the market, the monopoly firm can decide either to fight or to accommodate. The payoffs are the following: (2,0) if E does not enter; (-1, -1) if E enters and M fights and finally (1, 1) if E enters and M accommodates. The following game tree can represent it:

<center>[[File:extensive1.png]]</center>

===Matching pennies===
We can also consider the matching pennies game. Here, the first player either chooses head or tail. The second player then also chooses head or tail. If both pennies have the same face, the second player wins; if not, the player 1 wins. A variant of this game can be that both players choose at the same time. The second player thus chooses without knowing the result of the first player (it is represented on the second graph). It is important to notice that the resulting payoffs are the same in both cases.

<center>[[File:extensive2.png]]</center>

==Typology==

===Perfect and complete information===
It exists different types of extensive form games. Indeed, in some games, all the players know exactly each move of the others. The information is thus perfect and they can base their decision on the past moves of others. Moreover, if every player is aware of the entire tree (nothing is hidden or related to the chance), the game will be complete. For example, the chess game is perfect and complete. Indeed, each player knows the moves of the opponent and everyone knows all the possible moves they can achieve. It is also the case of the entry game explained above. In conclusion, all the information sets here is a singleton.

===Imperfect information===
Sometimes, it happens that one or several players do not get the perfect information. Indeed, it is possible that when a player has to decide, he does not know the past decision of the other player. In other words, a player sometimes cannot observe the choice of another player. Therefore, it means that moves can be simultaneous or a move could be hidden. The information set here will not be a singleton anymore. Graphically, it is represented by a dotted line connecting all the nodes of the information set (as on the tree of the variant of the matching pennies game). In conclusion, if a game is composed from at least one information set with more than one node, the game has imperfect information.

===Incomplete information===
In some games, it is also possible that some information is missing. For example, it is possible that a player does not know all the payoffs of the game. Some other information can also be missing: available nodes or decisions, the type or number of other players, the decision order, etc. In order to determine the type of the players, a so-called “nature” can be used (represented by a non-filled node) using a probability distribution. Here, each player observes his type but the other players do not. In conclusion, as we know that the payoff of the terminal node depends of the type of the player, nobody is sure about the payoff matrix. The game has thus incomplete information. An example of this is the auction game.

===Finite or infinite games===
A last typology can distinguish finite and infinite games. In the first case, there is a finite set of actions at each decision node. In the latter case, it can arise that at a decision node, there is an infinite number of possible actions. For example, if we have a Stackelberg competition, we can imagine that the decision node will be to define the quantity to produce. However, these quantities can take infinite value.

==Strategies==
A strategy is a complete contingent plan explaining what a player will do in every situation. Thus, for all the information sets, we can express the strategies as the different possible decision that the player can make.

===Pure strategy===
If we continue with the formal notation, we can define a pure strategy for a player i as a function si: Hi → Ai such that si(h) ∈ A(h) for each h ∈ Hi.
Let Si denote the set of pure strategies available to player i, and S = S1 × ... × SI denote the set of pure strategy profiles. As before, we will let s = (s1, ..., sI ) denote a strategy profile, and s−i the strategies of i’s opponents. For example, if we take the entry game, here are the strategies of both players:
S1=[out-fight; out-accommodate; in-fight; in-accommodate]
S2=[in-out]
We can notice here that if we make a list of all players and their pure strategies, we can represent the extensive form game with its associated normal form.

===Mixed strategy===
A mixed strategy for player i in an extensive form game is a probability distribution over pure strategies, i.e. some σi ∈ ∆(Si).
In a mixed strategy, the player randomly chooses at the beginning a pure strategy that he will use afterwards. When this strategy is chosen, he continues by following this deterministic rule of decisions.

===Behavioural strategy===
A behavioural strategy for player i in an extensive form game is a function σi : Hi → ∆(Ai) such that support(σi(h)) ⊂ A(h) for all h ∈ Hi.
On the opposite, a behavioural strategy can be seen as stochastic. Indeed, here a random decision will be made at each decision node. Here, the hazard is focused on the next action and not on a global rule of behaviour as for mixed strategy.

There is a theorem linking these two types of strategies: the Kuhn’s Theorem. It says that if we have a game with perfect recall (i.e. players always remember past decision and information they had while making those decisions), mixed and behavioural strategies are equivalent. It means that there is an equivalent behavioural strategy for any mixed strategy.

==Strategic form of extensive form games==
In order to solve extensive form games, we can also use the concept of Nash equilibrium of the normal form, as explained above. We will also show in the next sections that it allows providing more detailed predictions (e.g. sub-game perfect equilibrium). Let us take again the entry game example. Gathering all the strategies, we can build the associated normal form as follow:

<center>
{| border="1"
|
|'''Allow'''
|'''Fight'''
|-
|'''In'''
|align="center"|(2,1)
|align="center"|(0,0)
|-
|'''Out'''
|align="center"|(1,2)
|align="center"|(1,2)
|}
</center>

Therefore, now that we transformed the extensive form game, we can analyse it and see that there are two pure Nash equilibria (Challenge-Accommodate and Stay out-Fight). However, this is not completely right. Indeed, using the normal form, the Nash equilibria do not take into account the sequential structure of that game. It treats strategies as choices that are decided in one time and forever. Thus, we need an equilibrium that gives optimal strategies for all players not only at start but also at every moment of history. To do this, we first need to define the concept of sub-game.

==Sub-game==
A sub-game is a part of the game that can be seen as a game itself. It owns a single initial node and includes all the successive nodes starting from there. In other words, when the initial node of a sub-game is reached, players can focus only on it and forget the past history of the game. Again, we can give the formal notation of a sub-game:
Let G be an extensive form game, a sub-game G′ of G consists of (i) a subset Y of the nodes X consisting of a single non-terminal node x and all of its successors, which has the property that if y ∈ Y, y′ ∈ h(y) then y′ ∈ Y , and (ii) information sets, feasible moves, and payoffs at terminal nodes as in G.
Let us illustrate it with an example:

<center>[[File:extensive3.png]]</center>

Here we can see that there are five different sub-games. First, there is the game itself (G). Second, we have a sub-game starting when C is selected at the first step (G4). Then, we have two different sub-games, depending of the decision of player 1 (G2 and G3). Finally, we have a last sub-game that includes the last decision of player 2. Doing this, we can refine the model and analyse if there is any sub-game perfect equilibrium. We can define a sub-game perfect equilibrium as follow (Selten, 1965): A sub-game perfect Nash equilibrium (SPNE) is a profile of strategies such that in each sub-game the induced strategy profile is a Nash equilibrium of that sub-game. Moreover, we can add that in every extensive form game there is at least one sub-game perfect equilibrium. Now we are therefore able to refine the Nash equilibria in order to define the more precise equilibria. To achieve this, we can use the backward induction methodology, describe in the following section.

==Backward induction==
Basically, the backward induction process is an iterative method in order to find the optimal strategies and Nash equilibria in extensive form or sequential games. The principle is quite simple: we first start by defining the optimal strategy of the player that makes the last move. Regarding this decision, we analyse the optimal strategy for the player that makes the previous move. In other words, what would he do knowing the optimal strategy of the other player. Finally, we continue this process till we reach the initial node. Doing this, we can determine the Nash equilibria of each sub-game of the original game. At the end, we will be able to define the sub-game perfect equilibrium.

Let us illustrate this with a new example. Consider the following game:

<center>[[File:extensive4.png]]</center>

In this extensive form game, the first player chooses one action (C or D). Depending of this, the second player chooses his final action (E or F). The different payoffs are at the bottom of the graph. Here, we can see that we have three sub-games (the game itself and the two sub-games, depending on the player 1’s decision.

<center>[[File:extensive5.png]]</center>

We start by analysing the two different sub-games. In the first one, if player 1 chooses action C, the second player will automatically choose the action E because it gives a better payoff (1 > 0). In the other sub-game on the opposite, if player 1 chooses D, the player 2 will choose action F for the same reason as the previously (3 > 2). Now that we have the optimal strategies for the last move, we can go upstream in order to find the optimal strategy of player 1. To do this, we compare his payoff in both situations. If he chooses the action C, the player 1 will get a utility of 2. In the other case, he will receive only 1. Player 1 will thus decide to take the action C because he knows that doing this, the second player will choose E and then he will get a better payoff. The strategy (C-E) is therefore the sub-game perfect equilibrium. In this case, it is the only sub-game perfect equilibrium.
However the backward induction cannot be applied to every extensive form games. Indeed, sometimes if the game is infinitely long, it will be impossible to determine the sub-game perfect equilibria. However, it is possible to apply this methodology even if we have an imperfect information game.

==Chance moves==
A last concept that is important to stress out is that sometimes it is possible that chance nodes appear in the extensive form game. Indeed, depending on a choice, it is possible to reach different path according to a probability function.

<center>[[File:extensive6.png]]</center>

We can observe in this game that if the first player chooses the action B, we reach the chance node. There is 50% of chance that the game stops with a certain payoff (3,0) and 50% of chance that the second player has to make a final decision. Here, we can also apply the backward induction to find the sub-game perfect equilibrium. Let us start with the final sub-game. The second player will automatically choose action C because it gives a better payoff. Knowing this, the first player has two possibilities. First, he can choose action A and the game end with the payoff (1,1). Second, he can decide to go on the chance node. In this case, he has 50% chance to get a utility of 3 but 50% chance to receive nothing. The total utility is thus 50% of 3 + 50% of 0 = 1,5. This payoff is better than 1 if he chooses action A and will thus decide to take action B. The perfect equilibrium here is thus (A-C).

==Exercises==
:'''1. Consider the following extensive form game:'''

<center>[[File:extensive7.png]]</center>

:a) Find all the Nash equilibria of the game
:b) Find all the sub-game perfect equilibria of the game

:'''2. In an extensive form game two nodes are in the same information set whenever'''

:(a) They belong to different players and players cannot differentiate between them.
:(b) They belong to the same player and that player cannot differentiate be- tween them.
:(c) They belong to different players and players can differentiate between them.
:(d) They belong to the same player and that player can differentiate between them.
:(e) None of the above.

:'''3. If we solve the following game with backwards induction, what is the resulting payoff?'''

<center>[[File:extensive8.png]]</center>

==References==
*Levin, J. (2002). Extensive form games, seen on http://www.stanford.edu/~jdlevin/Econ%20203/ExtensiveForm.pdf the 4th of January
*Ratliff, J. (1997). Strategies in Extensive-Form Games, seen on http://www.virtualperfection.com/gametheory/4.2.StrategiesInExtensiveFormGames.1.0.pdf the 4th of January
*Lenaerts, T. (2012). Learning Dynamics, seen on http://ai.vub.ac.be/sites/default/files/Extensive%20form.pdf the 5th of January

File:Extensive8.png

2013-01-06T11:49:24Z

Qantw00:

File:Extensive7.png

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File:Extensive5.png

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File:Extensive4.png

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File:Extensive3.png

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Qantw00:

Extensive form

2013-01-06T11:37:42Z

Qantw00: Created page with "__TOC__ ==Introduction== The normal form games give a representation of players that make decisions simultaneously. However, in these games, players do not have any informatio..."

__TOC__
==Introduction==
The normal form games give a representation of players that make decisions simultaneously. However, in these games, players do not have any information about the other players’ strategies when they make their own choice. However, in lots of different situations, players make their decisions depending of the past choices of other players (e.g. chess game, auctions, negotiation, etc.). To represent this kind of games, we can use the extensive form by implementing game trees. In this paper, we will first define the concept of extensive form game. After illustrating it with some concrete examples, we will describe the typology and the different variants that can exist in this kind of games. Fourth, we will analyze more in detail the notion of strategy. Finally, we will study how we can solve this kind of games by introducing the concept of backward induction.

==Definition==
An extensive form game will be composed by several main components:
*Players: more often we consider games with two players.
*Procedure: who moves when and what are the possible choices are questions that have to be defined in the game.
*Information: it is important to know if we are in a situation with perfect and complete information or not.
*History: is the sequence of actions taken by the players up to some decision point. A terminal history is a history that contains the action choices of all the players up until the point where the payoff is distributed.
*Payoffs: finally, it is crucial to determine the different payoffs in function of the decisions made.

Here, we use the game trees in order to represent the extensive form games. The decisions are made at the nodes included in the set X. There is also an initial node at which the game begins. Then, the game evolves from node to node depending on the players’ decisions. The game ends when a terminal node is reached (set Z). At this point, players receive a payoff corresponding to the terminal node. The preferences of players (i = 1…I) are represented by utility functions ui. When a player has to decide, he might not know exactly at which of the nodes it’s located. There are thus information sets (set of nodes that all belong to the same player and at all of which the same set of action is available). We can thus observe that this kind of games can be divided into smaller sub-games that represent sub-trees according to the different information sets.

Now that the background is set, let us express the extensive form games in a formal notation. Here, the methodology of Levin (2002) will be used:
*A set of players i = 1, …, I
*A finite set X of nodes that form the game tree, with Z ⊂ X being the terminal nodes.
*A set of functions that describe for each x ∉ Z,
:The player i(x) who moves at x.
:The set A(x) of possible actions at x.
:The successor node n(x, a) resulting from action a.
*Payoff functions ui : Z → ℜ assigning payoffs to players as a function of the terminal node reached.
*An information partition: for each x, let h(x) denote the set of nodes that are possible given what player i(x) knows. Thus, if x′ ∈ h(x), then i(x′) = i(x), A(x′) = A(x) and h(x′) = h(x).
We can also use the notation i(h) or A(h) to denote the player who moves at information set h and his set of possible actions.

==Concrete examples==

===Entry game===
There is a firm M that has a monopoly on the market. Another firm E can decide to enter or not this market. If the firm E decides to enter the market, the monopoly firm can decide either to fight or to accommodate. The payoffs are the following: (2,0) if E does not enter; (-1, -1) if E enters and M fights and finally (1, 1) if E enters and M accommodates. The following game tree can represent it:

===Matching pennies===
We can also consider the matching pennies game. Here, the first player either chooses head or tail. The second player then also chooses head or tail. If both pennies have the same face, the second player wins; if not, the player 1 wins. A variant of this game can be that both players choose at the same time. The second player thus chooses without knowing the result of the first player (it is represented on the second graph). It is important to notice that the resulting payoffs are the same in both cases.

==Typology==

===Perfect and complete information===
It exists different types of extensive form games. Indeed, in some games, all the players know exactly each move of the others. The information is thus perfect and they can base their decision on the past moves of others. Moreover, if every player is aware of the entire tree (nothing is hidden or related to the chance), the game will be complete. For example, the chess game is perfect and complete. Indeed, each player knows the moves of the opponent and everyone knows all the possible moves they can achieve. It is also the case of the entry game explained above. In conclusion, all the information sets here is a singleton.

===Imperfect information===
Sometimes, it happens that one or several players do not get the perfect information. Indeed, it is possible that when a player has to decide, he does not know the past decision of the other player. In other words, a player sometimes cannot observe the choice of another player. Therefore, it means that moves can be simultaneous or a move could be hidden. The information set here will not be a singleton anymore. Graphically, it is represented by a dotted line connecting all the nodes of the information set (as on the tree of the variant of the matching pennies game). In conclusion, if a game is composed from at least one information set with more than one node, the game has imperfect information.

===Incomplete information===
In some games, it is also possible that some information is missing. For example, it is possible that a player does not know all the payoffs of the game. Some other information can also be missing: available nodes or decisions, the type or number of other players, the decision order, etc. In order to determine the type of the players, a so-called “nature” can be used (represented by a non-filled node) using a probability distribution. Here, each player observes his type but the other players do not. In conclusion, as we know that the payoff of the terminal node depends of the type of the player, nobody is sure about the payoff matrix. The game has thus incomplete information. An example of this is the auction game.

===Finite or infinite games===
A last typology can distinguish finite and infinite games. In the first case, there is a finite set of actions at each decision node. In the latter case, it can arise that at a decision node, there is an infinite number of possible actions. For example, if we have a Stackelberg competition, we can imagine that the decision node will be to define the quantity to produce. However, these quantities can take infinite value.

==Strategies==
A strategy is a complete contingent plan explaining what a player will do in every situation. Thus, for all the information sets, we can express the strategies as the different possible decision that the player can make.

===Pure strategy===
If we continue with the formal notation, we can define a pure strategy for a player i as a function si: Hi → Ai such that si(h) ∈ A(h) for each h ∈ Hi.
Let Si denote the set of pure strategies available to player i, and S = S1 × ... × SI denote the set of pure strategy profiles. As before, we will let s = (s1, ..., sI ) denote a strategy profile, and s−i the strategies of i’s opponents. For example, if we take the entry game, here are the strategies of both players:
S1=[out-fight; out-accommodate; in-fight; in-accommodate]
S2=[in-out]
We can notice here that if we make a list of all players and their pure strategies, we can represent the extensive form game with its associated normal form.

===Mixed strategy===
A mixed strategy for player i in an extensive form game is a probability distribution over pure strategies, i.e. some σi ∈ ∆(Si).
In a mixed strategy, the player randomly chooses at the beginning a pure strategy that he will use afterwards. When this strategy is chosen, he continues by following this deterministic rule of decisions.

===Behavioural strategy===
A behavioural strategy for player i in an extensive form game is a function σi : Hi → ∆(Ai) such that support(σi(h)) ⊂ A(h) for all h ∈ Hi.
On the opposite, a behavioural strategy can be seen as stochastic. Indeed, here a random decision will be made at each decision node. Here, the hazard is focused on the next action and not on a global rule of behaviour as for mixed strategy.

There is a theorem linking these two types of strategies: the Kuhn’s Theorem. It says that if we have a game with perfect recall (i.e. players always remember past decision and information they had while making those decisions), mixed and behavioural strategies are equivalent. It means that there is an equivalent behavioural strategy for any mixed strategy.

==Strategic form of extensive form games==
In order to solve extensive form games, we can also use the concept of Nash equilibrium of the normal form, as explained above. We will also show in the next sections that it allows providing more detailed predictions (e.g. sub-game perfect equilibrium). Let us take again the entry game example. Gathering all the strategies, we can build the associated normal form as follow:

Allow Fight
In 2,1 0,0
Out 1,2 1,2

Therefore, now that we transformed the extensive form game, we can analyse it and see that there are two pure Nash equilibria (Challenge-Accommodate and Stay out-Fight). However, this is not completely right. Indeed, using the normal form, the Nash equilibria do not take into account the sequential structure of that game. It treats strategies as choices that are decided in one time and forever. Thus, we need an equilibrium that gives optimal strategies for all players not only at start but also at every moment of history. To do this, we first need to define the concept of sub-game.

==Sub-game==
A sub-game is a part of the game that can be seen as a game itself. It owns a single initial node and includes all the successive nodes starting from there. In other words, when the initial node of a sub-game is reached, players can focus only on it and forget the past history of the game. Again, we can give the formal notation of a sub-game:
Let G be an extensive form game, a sub-game G′ of G consists of (i) a subset Y of the nodes X consisting of a single non-terminal node x and all of its successors, which has the property that if y ∈ Y, y′ ∈ h(y) then y′ ∈ Y , and (ii) information sets, feasible moves, and payoffs at terminal nodes as in G.
Let us illustrate it with an example:

Here we can see that there are five different sub-games. First, there is the game itself (G). Second, we have a sub-game starting when C is selected at the first step (G4). Then, we have two different sub-games, depending of the decision of player 1 (G2 and G3). Finally, we have a last sub-game that includes the last decision of player 2. Doing this, we can refine the model and analyse if there is any sub-game perfect equilibrium. We can define a sub-game perfect equilibrium as follow (Selten, 1965): A sub-game perfect Nash equilibrium (SPNE) is a profile of strategies such that in each sub-game the induced strategy profile is a Nash equilibrium of that sub-game. Moreover, we can add that in every extensive form game there is at least one sub-game perfect equilibrium. Now we are therefore able to refine the Nash equilibria in order to define the more precise equilibria. To achieve this, we can use the backward induction methodology, describe in the following section.

==Backward induction==
Basically, the backward induction process is an iterative method in order to find the optimal strategies and Nash equilibria in extensive form or sequential games. The principle is quite simple: we first start by defining the optimal strategy of the player that makes the last move. Regarding this decision, we analyse the optimal strategy for the player that makes the previous move. In other words, what would he do knowing the optimal strategy of the other player. Finally, we continue this process till we reach the initial node. Doing this, we can determine the Nash equilibria of each sub-game of the original game. At the end, we will be able to define the sub-game perfect equilibrium.

Let us illustrate this with a new example. Consider the following game:

In this extensive form game, the first player chooses one action (C or D). Depending of this, the second player chooses his final action (E or F). The different payoffs are at the bottom of the graph. Here, we can see that we have three sub-games (the game itself and the two sub-games, depending on the player 1’s decision.

We start by analysing the two different sub-games. In the first one, if player 1 chooses action C, the second player will automatically choose the action E because it gives a better payoff (1 > 0). In the other sub-game on the opposite, if player 1 chooses D, the player 2 will choose action F for the same reason as the previously (3 > 2). Now that we have the optimal strategies for the last move, we can go upstream in order to find the optimal strategy of player 1. To do this, we compare his payoff in both situations. If he chooses the action C, the player 1 will get a utility of 2. In the other case, he will receive only 1. Player 1 will thus decide to take the action C because he knows that doing this, the second player will choose E and then he will get a better payoff. The strategy (C-E) is therefore the sub-game perfect equilibrium. In this case, it is the only sub-game perfect equilibrium.
However the backward induction cannot be applied to every extensive form games. Indeed, sometimes if the game is infinitely long, it will be impossible to determine the sub-game perfect equilibria. However, it is possible to apply this methodology even if we have an imperfect information game.

==Chance moves==
A last concept that is important to stress out is that sometimes it is possible that chance nodes appear in the extensive form game. Indeed, depending on a choice, it is possible to reach different path according to a probability function.

We can observe in this game that if the first player chooses the action B, we reach the chance node. There is 50% of chance that the game stops with a certain payoff (3,0) and 50% of chance that the second player has to make a final decision. Here, we can also apply the backward induction to find the sub-game perfect equilibrium. Let us start with the final sub-game. The second player will automatically choose action C because it gives a better payoff. Knowing this, the first player has two possibilities. First, he can choose action A and the game end with the payoff (1,1). Second, he can decide to go on the chance node. In this case, he has 50% chance to get a utility of 3 but 50% chance to receive nothing. The total utility is thus 50% of 3 + 50% of 0 = 1,5. This payoff is better than 1 if he chooses action A and will thus decide to take action B. The perfect equilibrium here is thus (A-C).

==Exercises==
1) Consider the following extensive form game:

a) Find all the Nash equilibria of the game
b) Find all the sub-game perfect equilibria of the game

2) In an extensive form game two nodes are in the same information set whenever

(a) They belong to different players and players cannot differentiate between them.
(b) They belong to the same player and that player cannot differentiate be- tween them.
(c) They belong to different players and players can differentiate between them.
(d) They belong to the same player and that player can differentiate between them.
(e) None of the above.

3) If we solve the following game with backwards induction, what is the resulting payoff?

==References==
*Levin, J. (2002). Extensive form games, seen on http://www.stanford.edu/~jdlevin/Econ%20203/ExtensiveForm.pdf the 4th of January
*Ratliff, J. (1997). Strategies in Extensive-Form Games, seen on http://www.virtualperfection.com/gametheory/4.2.StrategiesInExtensiveFormGames.1.0.pdf the 4th of January

Assignments WS 2012/2013

2012-12-06T18:32:00Z

Qantw00: /* Enter the market or not? */

{{Ambox
| text = <div>
Add your proposals to this page. Do not forget to sign your content. You can use <nowiki>~~~~</nowiki> (four tildas) to sign your post automatically. Use Show preview to check your content until you decide to send the post finally.
</div>
}}

{{Ambox
| text = <div>
Please, try to formulate the assignment carefully. It is your semestral paper, so considerble effort invested into the assignment is expected. Bear in mind that a research report is your main output, thus your model should provide figures that are specific, measurable and verifiable enough. Think carefully about the way you will create your model, derive entities you will use, draw a sketch of the model, estimate what you will measure. When you have a good notion about the model, submit your assignment. And of course, do not forget to read [[How to deal with the simulation assignment]].
</div>
}}

== A local restaurant during lunchtime ==

In the place I live is a restaurant which serves lunches during lunchtime. There are places for 40 visitors, 10 tables, 1 kitchen and 1 bar, 2 waiters, 2 chiefs, 6 items on the lunch menu and 10 items on a beverage menu.

Entities, attributes and constraints:

'''Visitor'''
* he has to decide what he wants to order (more items on the menu = more time to decide)
* can order any item from the menu and any item from the beverage menu
* he's got just 30 minutes for the lunch because he works and his time for the lunch is limited
* after 30 minutes he's getting angry
* prefers seat alone at the table (see Table bellow)
* if the restaurant is crowded (or full) he could be unsatisfied

'''Waiter'''
* receives orders from visitors
* put orders to the kitchen
* serve orders from kitchen to the table (visitor)

'''Cook'''
* works in the kitchen
* prepares lunches
* the more kinds of lunches, the more time to prepare or cook the lunch

'''Table'''
* provides 1-4 places for visitors
* they are placed in the restaurant and each of them has different distance from kitchen and bar
* more tables = more places for seat = more visitors

The simulation goal is to set a real model of the restaurant and try to find a better optimum of menu items/waiters count/cooks count related to customers satisfaction.

'''Tomas, what's now? :)'''

Thank you.

[[User:Jirihradil|Jiří Hradil]] 10:23, 5 December 2012 (CET)
:OK, what simulation tool would you prefer to use for it? [[User:Tomáš|Tomáš]] 11:21, 6 December 2012 (CET)

::Sorry Tomas, I'm going to use Netlogo for it. May I understand it that you have accepted the simulation? Thank you. [[User:Jirihradil|Jiří Hradil]] 11:33, 6 December 2012 (CET)
:::I think Simprocess would be much better platform for this. I don't see there enough true "agent" characteristics. If you are willing to make it in Simprocess, it is '''accepted'''. Please, try to keep as many real parameters as possible. If you still would prefer NetLogo, please, try to explain what benefit do you see in making it in this tool. [[User:Tomáš|Tomáš]] 14:11, 6 December 2012 (CET)
::::In Netlogo I can simulate avoiding of waiters if they cross themselves, avoiding guests, compute distances between waiters, tables and kitchen using vectors, simulate walking in space and so on. For example more guests will slow down the restaurant because they can run into others and so on. I think that Simprocess is not a right tool for it because it can't describe reality as it is. I really hope that you trust me that I will do it in the right and proper way. [[User:Jirihradil|Jiří Hradil]] 14:26, 6 December 2012 (CET)
:::::All right, but bear in mind that if you stipulate it this way, it means a simulation of agent movement, avoidance, etc. etc. It could be a pretty complex problem with several hidden pitfalls if you want to make it realistic. If it is OK for you, then '''accepted''' and good luck.[[User:Tomáš|Tomáš]] 14:58, 6 December 2012 (CET)

== Hive ==
'''author'''
:--[[User:Xseda07|Adam Sedláček (xseda07)]] 12:09, 30 November 2012 (CET)
<div>
As is known, the hive is a community that is very complex and is influenced by both internal and external factors. Therefore, I propose to create a simulation that would examine the influence of internal and external circumstances which influence the hive and the ecosystem in which they live. Especially I mean these factors:
<ul>
<li>Number and distance of flowers and fruit trees to pollinate</li>
<li> number of workers and drones in the hive
<li> how early beginning / end of summer / winter affect stocks of honey and colony survival
<li>how number of workers affect pollination of trees/ flowers and therefore the number of flowers and trees in neighbourhood
</ul>
<div>
'''How it will work'''
<div>
Workers are responsible for getting food for whole hive and also for pollination of trees and flowers. They are using sun for the orientation and they communicate between themselves. In the beehive there ale drones, which fertilizes Bee´s queen, bee´s queen, which oviposits and the eggs-larvas, which are later transformed to either workers or drones.
<div>
Trees/flowers need to be pollinated in order to proliferate. There will be also change of season and different hive behaviour during summer/winter
<div>
'''Method'''
I will use NetLogo to simulate the Hive
:OK, sounds interesting. '''Accepted'''. Please, identify yourself. [[User:Tomáš|Tomáš]] 22:49, 29 November 2012 (CET)
::I am sorry. --[[User:Xseda07|Adam Sedláček (xseda07)]] 12:09, 30 November 2012 (CET)

==To vote or not to vote? ==

'''author'''
:--[[User:Iuter88|Riccardo Torchio)]] 15:53, 3/12/2012 (CET)
<div>
I want to design a simulation that can show us how people decide if to go to vote or not.

I will create agent with
-proximity to a person that can influence the agent
-willingness to go to vote
-expected result of the vote
I can take my conclusion about the threshold value of this 3 variables in this process.
<div>
'''Method'''
i will use NetLogo to simulate the process
:Generally it could be a good idea, but you should elaborate it into a greater detail. Since it is a "soft" problem, it is ambiguous. How it will be connected with reality? How you can evaluate your results? What you are going to measure? If you stick to this topic, the best idea would be to find a scientific article or an experiment where similar problem is explored and to design your task accordingly - on its basis.
:If you just create what you have suggested, well, you will have a nice NetLogo model. What's the point? Please, think twice about it.
:[[User:Tomáš|Tomáš]] 12:16, 4 December 2012 (CET)
==Default==
'''author'''
:--[[User:Iuter88|Riccardo Torchio)]] 18:34, 4/12/2012 (CET)
<div>
'''topic'''
As a second proposal i'm thinking about a simulation of default by a state.
My agents will be:
- banks
-citizens

The news of the dafault could be placed in a randomly around. At this point the agents
that enter in contact with the news will run to bank to withdraw theyr money.
If someone see queue at the banks will help the process to speed up, entering the queue.
I can take some conclusion about the self-fulfilling prophecy of a default by banks and
how people react to this news.
<div>
'''Method'''
i will use NetLogo to simulate the process

:Bank runs are generally a perfect phenomenon to simulate. I like the idea, however I don't see there a major benefit to make it as agent based simulation particularly in NetLogo. What I would recommend is to wait until you first systems dynamics class (tomorrow I guess) and to try to consider creating it using Vensim. [[User:Tomáš|Tomáš]] 15:08, 6 December 2012 (CET)

==Enter the market or not?==
I was thinking about a firms competition simulation. A first firm decides to enter the market or not and depending on the choice, the firm already in the market decides to fight or to accommodate the new firm. For example, I could take the example of fast-food in Belgium: the burger king chain could be trying to enter the market and thus the McDonald's chain already present could decide of its behavior.

Wagon Antoine
[[User:Qantw00|Qantw00]] 22:10, 3 December 2012 (CET)
:Good idea, Antoine, but you should elaborate it into a greater detail. It is too vague so far. What will be the entities, how you will treat products, how you will work with prices, what will be a role of customers...?
:I really like the thought, however market simulations are always complicated, because people usually tend to add more and more details. You should imagine, how it should work and find a reasonable and well defined situation what you will simulate.
:You can also wait for you systems dynamics class. Perhaps it could be a proper approach for your idea.
:[[User:Tomáš|Tomáš]] 12:30, 4 December 2012 (CET)

Basically, here is how will work my simulation (can be improved in the future of course):

* At the beginning, there are only McDonald's firms on the market. They decide on the location, the price and the quality of the products.
* The customer decides to go to a restaurant regarding the location, price and quality
* At the second step, Burger King decides to open a restaurant or not. if yes, it has to choose of course the location, price and quality.
* They, when there are the two brands on the market (McDonald's and Burger King), McDonald's will decide if they fight or accommodate. if they find, they will either provide a lower price or a better quality for the same price. if they accommodate they will change their features in order to get the same as Burger King and thus split the market.
* Both brands can also decide to open new restaurants.

The goal for each brand will be to get the best market share.

I think that Netlogo is the most suitable platform for this simulation. I don't know if it is realistic and feasible; I just tried to gather some ideas for the simulation. Thus what do you think about it?

Wagon Antoine [[User:Qantw00|Qantw00]] 19:31, 6 December 2012 (CET)

== Disease ==
'''author'''
--[[User:Pilar|Pilar]] 10:57, 4 December 2012 (CET)

'''Subject of simulation'''

I would like to simulate spread of a disease which would take incubation period (i.e. person is acting as carrier of the disease but doesn't have any symptoms) and immunity into account as suggested in ''Modelování a siulace komplexních systémů'' by Radek Pelánek. The simulation will be based on SIRS model of diseases with constant population (simulating period of weeks or months and non-lethal diseases).

'''Objectives'''

To determine influence of relative length of incubation period, duration of disease and duration of immunity on the dynamics of the disease in given population - will any patterns develop, when do more or less people become ill, can the disease die out in given population?

'''Method'''

MAS with random contact of agents.

:First, I think it was already used in the past, and second: it is better to create your own original assignment. However, you definitely can use it as an inspiration and redefine it into something new, what would be derived from this idea.
:[[User:Tomáš|Tomáš]] 21:23, 4 December 2012 (CET)

== Blood type ==
'''Author''' --[[User:Xmacm45|Xmacm45]] 10:12, 5 December 2012 (CET)
<div>
The most importanat blood-group system is ABO system. Its named after 4 blood group:

<ul>
<li>0</li>
<li>A</li>
<li>B</li>
<li>AB</li>
</ul>
<div>
Each of this group (past 0) where evoluted from "0" type by adding antibodies A, B and combination of both. The system of inheritance blood group have exact rules by accepting one allele from each parent. Because of evolution, the groups are increasing and decreasing the amount of its representative. Id like to predict, based on multi-agent model simulation, the future statistics and possibility of disappearance one of group (0).

'''Method'''
<div>

Id like to use NetLogo to simulate the evolution of blood groups
--Marta Machová 10:19, 5 December 2012 (CET)
:I like the idea, however from my point of view systems dynamics with Vensim would be perhaps more convenient tool for this. Oleg, what do you think?[[User:Tomáš|Tomáš]] 11:24, 6 December 2012 (CET)
::I think, that the multi-agent approach is more appropriate. As I understand it, this simulation would be simulated by many agents whose property would be the different blood type. So it is not about relations among several entities, but about greater number of entities which randomly meet and create a new entity with some blood type. [[User:Oleg.Svatos|Oleg.Svatos]] 18:24, 6 December 2012 (CET)

== Landscaping the areas ==
Landscaping workers create new functional outdoor areas. Their duties include planting bushes, trees, sod, and other forms of vegetation. Requirements of the project: number of planted stocks of trees, bushes etc. (or m2 of planted area). The ideal time to plant trees is early spring before budbreak (number of days or months).

'''Elements of this model:'''
experienced and new workers, productivity of workers, assimilation rate, planting rate, different overhead parameters (training new workers, weather conditions etc.)

'''The goal of the simulation:'''
Simulating and testing the model, set the different parameters, comparison of results and finding the optimal solution. I'd like to use as an inspiration model "Brooks’s Law Model".

'''Simulation environment'''
Vensim
--[[User:xachi01|Achatov Igor]] 14:00, 5 December 2012 (CET)

:I don't exactly get who would be this simulation for (who the target user is) and what are exactly the parameters it would help to set up. [[User:Oleg.Svatos|Oleg.Svatos]] 19:00, 6 December 2012 (CET)

== Fission-fusion society ==
This form of social organization occurs in several species of primates (chimpanzees, bonobos, ...). These societies change frequently in their size and composition due to changes in their environment and/or due to individual animal dynamics.

'''Elements of this model:'''
primates, sources of food, predators

'''The goal of the simulation:'''
Simulating societies and testing how they react to changing conditions (parameters). Also compare model to real life data (behavior of animals/groups, size of groups).

'''Method'''
NetLogo
[[User:Xpalj 24|Xpalj 24]] 20:15, 5 December 2012 (CET)
:OK, it could be... Please, just describe in more detail how the simulation should look and work. [[User:Tomáš|Tomáš]] 15:42, 6 December 2012 (CET)

Assignments WS 2012/2013

2012-12-06T18:31:05Z

Qantw00: /* Enter the market or not? */

{{Ambox
| text = <div>
Add your proposals to this page. Do not forget to sign your content. You can use <nowiki>~~~~</nowiki> (four tildas) to sign your post automatically. Use Show preview to check your content until you decide to send the post finally.
</div>
}}

{{Ambox
| text = <div>
Please, try to formulate the assignment carefully. It is your semestral paper, so considerble effort invested into the assignment is expected. Bear in mind that a research report is your main output, thus your model should provide figures that are specific, measurable and verifiable enough. Think carefully about the way you will create your model, derive entities you will use, draw a sketch of the model, estimate what you will measure. When you have a good notion about the model, submit your assignment. And of course, do not forget to read [[How to deal with the simulation assignment]].
</div>
}}

== A local restaurant during lunchtime ==

In the place I live is a restaurant which serves lunches during lunchtime. There are places for 40 visitors, 10 tables, 1 kitchen and 1 bar, 2 waiters, 2 chiefs, 6 items on the lunch menu and 10 items on a beverage menu.

Entities, attributes and constraints:

'''Visitor'''
* he has to decide what he wants to order (more items on the menu = more time to decide)
* can order any item from the menu and any item from the beverage menu
* he's got just 30 minutes for the lunch because he works and his time for the lunch is limited
* after 30 minutes he's getting angry
* prefers seat alone at the table (see Table bellow)
* if the restaurant is crowded (or full) he could be unsatisfied

'''Waiter'''
* receives orders from visitors
* put orders to the kitchen
* serve orders from kitchen to the table (visitor)

'''Cook'''
* works in the kitchen
* prepares lunches
* the more kinds of lunches, the more time to prepare or cook the lunch

'''Table'''
* provides 1-4 places for visitors
* they are placed in the restaurant and each of them has different distance from kitchen and bar
* more tables = more places for seat = more visitors

The simulation goal is to set a real model of the restaurant and try to find a better optimum of menu items/waiters count/cooks count related to customers satisfaction.

'''Tomas, what's now? :)'''

Thank you.

[[User:Jirihradil|Jiří Hradil]] 10:23, 5 December 2012 (CET)
:OK, what simulation tool would you prefer to use for it? [[User:Tomáš|Tomáš]] 11:21, 6 December 2012 (CET)

::Sorry Tomas, I'm going to use Netlogo for it. May I understand it that you have accepted the simulation? Thank you. [[User:Jirihradil|Jiří Hradil]] 11:33, 6 December 2012 (CET)
:::I think Simprocess would be much better platform for this. I don't see there enough true "agent" characteristics. If you are willing to make it in Simprocess, it is '''accepted'''. Please, try to keep as many real parameters as possible. If you still would prefer NetLogo, please, try to explain what benefit do you see in making it in this tool. [[User:Tomáš|Tomáš]] 14:11, 6 December 2012 (CET)
::::In Netlogo I can simulate avoiding of waiters if they cross themselves, avoiding guests, compute distances between waiters, tables and kitchen using vectors, simulate walking in space and so on. For example more guests will slow down the restaurant because they can run into others and so on. I think that Simprocess is not a right tool for it because it can't describe reality as it is. I really hope that you trust me that I will do it in the right and proper way. [[User:Jirihradil|Jiří Hradil]] 14:26, 6 December 2012 (CET)
:::::All right, but bear in mind that if you stipulate it this way, it means a simulation of agent movement, avoidance, etc. etc. It could be a pretty complex problem with several hidden pitfalls if you want to make it realistic. If it is OK for you, then '''accepted''' and good luck.[[User:Tomáš|Tomáš]] 14:58, 6 December 2012 (CET)

== Hive ==
'''author'''
:--[[User:Xseda07|Adam Sedláček (xseda07)]] 12:09, 30 November 2012 (CET)
<div>
As is known, the hive is a community that is very complex and is influenced by both internal and external factors. Therefore, I propose to create a simulation that would examine the influence of internal and external circumstances which influence the hive and the ecosystem in which they live. Especially I mean these factors:
<ul>
<li>Number and distance of flowers and fruit trees to pollinate</li>
<li> number of workers and drones in the hive
<li> how early beginning / end of summer / winter affect stocks of honey and colony survival
<li>how number of workers affect pollination of trees/ flowers and therefore the number of flowers and trees in neighbourhood
</ul>
<div>
'''How it will work'''
<div>
Workers are responsible for getting food for whole hive and also for pollination of trees and flowers. They are using sun for the orientation and they communicate between themselves. In the beehive there ale drones, which fertilizes Bee´s queen, bee´s queen, which oviposits and the eggs-larvas, which are later transformed to either workers or drones.
<div>
Trees/flowers need to be pollinated in order to proliferate. There will be also change of season and different hive behaviour during summer/winter
<div>
'''Method'''
I will use NetLogo to simulate the Hive
:OK, sounds interesting. '''Accepted'''. Please, identify yourself. [[User:Tomáš|Tomáš]] 22:49, 29 November 2012 (CET)
::I am sorry. --[[User:Xseda07|Adam Sedláček (xseda07)]] 12:09, 30 November 2012 (CET)

==To vote or not to vote? ==

'''author'''
:--[[User:Iuter88|Riccardo Torchio)]] 15:53, 3/12/2012 (CET)
<div>
I want to design a simulation that can show us how people decide if to go to vote or not.

I will create agent with
-proximity to a person that can influence the agent
-willingness to go to vote
-expected result of the vote
I can take my conclusion about the threshold value of this 3 variables in this process.
<div>
'''Method'''
i will use NetLogo to simulate the process
:Generally it could be a good idea, but you should elaborate it into a greater detail. Since it is a "soft" problem, it is ambiguous. How it will be connected with reality? How you can evaluate your results? What you are going to measure? If you stick to this topic, the best idea would be to find a scientific article or an experiment where similar problem is explored and to design your task accordingly - on its basis.
:If you just create what you have suggested, well, you will have a nice NetLogo model. What's the point? Please, think twice about it.
:[[User:Tomáš|Tomáš]] 12:16, 4 December 2012 (CET)
==Default==
'''author'''
:--[[User:Iuter88|Riccardo Torchio)]] 18:34, 4/12/2012 (CET)
<div>
'''topic'''
As a second proposal i'm thinking about a simulation of default by a state.
My agents will be:
- banks
-citizens

The news of the dafault could be placed in a randomly around. At this point the agents
that enter in contact with the news will run to bank to withdraw theyr money.
If someone see queue at the banks will help the process to speed up, entering the queue.
I can take some conclusion about the self-fulfilling prophecy of a default by banks and
how people react to this news.
<div>
'''Method'''
i will use NetLogo to simulate the process

:Bank runs are generally a perfect phenomenon to simulate. I like the idea, however I don't see there a major benefit to make it as agent based simulation particularly in NetLogo. What I would recommend is to wait until you first systems dynamics class (tomorrow I guess) and to try to consider creating it using Vensim. [[User:Tomáš|Tomáš]] 15:08, 6 December 2012 (CET)

==Enter the market or not?==
I was thinking about a firms competition simulation. A first firm decides to enter the market or not and depending on the choice, the firm already in the market decides to fight or to accommodate the new firm. For example, I could take the example of fast-food in Belgium: the burger king chain could be trying to enter the market and thus the McDonald's chain already present could decide of its behavior.

Wagon Antoine
[[User:Qantw00|Qantw00]] 22:10, 3 December 2012 (CET)
:Good idea, Antoine, but you should elaborate it into a greater detail. It is too vague so far. What will be the entities, how you will treat products, how you will work with prices, what will be a role of customers...?
:I really like the thought, however market simulations are always complicated, because people usually tend to add more and more details. You should imagine, how it should work and find a reasonable and well defined situation what you will simulate.
:You can also wait for you systems dynamics class. Perhaps it could be a proper approach for your idea.
:[[User:Tomáš|Tomáš]] 12:30, 4 December 2012 (CET)

Basically, here is how will work my simulation (can be improved in the future of course):
- At the beginning, there are only McDonald's firms on the market. They decide on the location, the price and the quality of the products.
- The customer decides to go to a restaurant regarding the location, price and quality
- At the second step, Burger King decides to open a restaurant or not. if yes, it has to choose of course the location, price and quality.
- They, when there are the two brands on the market (McDonald's and Burger King), McDonald's will decide if they fight or accommodate. if they find, they will either provide a lower price or a better quality for the same price. if they accommodate they will change their features in order to get the same as Burger King and thus split the market.
- Both brands can also decide to open new restaurants.

The goal for each brand will be to get the best market share.

I think that Netlogo is the most suitable platform for this simulation. I don't know if it is realistic and feasible; I just tried to gather some ideas for the simulation. Thus what do you think about it?

Wagon Antoine

== Disease ==
'''author'''
--[[User:Pilar|Pilar]] 10:57, 4 December 2012 (CET)

'''Subject of simulation'''

I would like to simulate spread of a disease which would take incubation period (i.e. person is acting as carrier of the disease but doesn't have any symptoms) and immunity into account as suggested in ''Modelování a siulace komplexních systémů'' by Radek Pelánek. The simulation will be based on SIRS model of diseases with constant population (simulating period of weeks or months and non-lethal diseases).

'''Objectives'''

To determine influence of relative length of incubation period, duration of disease and duration of immunity on the dynamics of the disease in given population - will any patterns develop, when do more or less people become ill, can the disease die out in given population?

'''Method'''

MAS with random contact of agents.

:First, I think it was already used in the past, and second: it is better to create your own original assignment. However, you definitely can use it as an inspiration and redefine it into something new, what would be derived from this idea.
:[[User:Tomáš|Tomáš]] 21:23, 4 December 2012 (CET)

== Blood type ==
'''Author''' --[[User:Xmacm45|Xmacm45]] 10:12, 5 December 2012 (CET)
<div>
The most importanat blood-group system is ABO system. Its named after 4 blood group:

<ul>
<li>0</li>
<li>A</li>
<li>B</li>
<li>AB</li>
</ul>
<div>
Each of this group (past 0) where evoluted from "0" type by adding antibodies A, B and combination of both. The system of inheritance blood group have exact rules by accepting one allele from each parent. Because of evolution, the groups are increasing and decreasing the amount of its representative. Id like to predict, based on multi-agent model simulation, the future statistics and possibility of disappearance one of group (0).

'''Method'''
<div>

Id like to use NetLogo to simulate the evolution of blood groups
--Marta Machová 10:19, 5 December 2012 (CET)
:I like the idea, however from my point of view systems dynamics with Vensim would be perhaps more convenient tool for this. Oleg, what do you think?[[User:Tomáš|Tomáš]] 11:24, 6 December 2012 (CET)
::I think, that the multi-agent approach is more appropriate. As I understand it, this simulation would be simulated by many agents whose property would be the different blood type. So it is not about relations among several entities, but about greater number of entities which randomly meet and create a new entity with some blood type. [[User:Oleg.Svatos|Oleg.Svatos]] 18:24, 6 December 2012 (CET)

== Landscaping the areas ==
Landscaping workers create new functional outdoor areas. Their duties include planting bushes, trees, sod, and other forms of vegetation. Requirements of the project: number of planted stocks of trees, bushes etc. (or m2 of planted area). The ideal time to plant trees is early spring before budbreak (number of days or months).

'''Elements of this model:'''
experienced and new workers, productivity of workers, assimilation rate, planting rate, different overhead parameters (training new workers, weather conditions etc.)

'''The goal of the simulation:'''
Simulating and testing the model, set the different parameters, comparison of results and finding the optimal solution. I'd like to use as an inspiration model "Brooks’s Law Model".

'''Simulation environment'''
Vensim
--[[User:xachi01|Achatov Igor]] 14:00, 5 December 2012 (CET)

:I don't exactly get who would be this simulation for (who the target user is) and what are exactly the parameters it would help to set up. [[User:Oleg.Svatos|Oleg.Svatos]] 19:00, 6 December 2012 (CET)

== Fission-fusion society ==
This form of social organization occurs in several species of primates (chimpanzees, bonobos, ...). These societies change frequently in their size and composition due to changes in their environment and/or due to individual animal dynamics.

'''Elements of this model:'''
primates, sources of food, predators

'''The goal of the simulation:'''
Simulating societies and testing how they react to changing conditions (parameters). Also compare model to real life data (behavior of animals/groups, size of groups).

'''Method'''
NetLogo
[[User:Xpalj 24|Xpalj 24]] 20:15, 5 December 2012 (CET)
:OK, it could be... Please, just describe in more detail how the simulation should look and work. [[User:Tomáš|Tomáš]] 15:42, 6 December 2012 (CET)

Assignments WS 2012/2013

2012-12-03T21:10:33Z

Qantw00:

''Add your proposals to this page. Do not forget to sign your content. You can use <nowiki>~~~~</nowiki> (four tildas) to sign your post automatically. Use ''Show preview'' to check your content until you decide to send the post finally.''

== War of the Elves ==

I would like to simulate a war between two kinds of Elves - The Black Race and the White Race. Every army has these kinds of soldiers:

* a warrior - armed with a sword, health 10, strength 5
* an archer - armed with a bow, health 5, strength 10
* a wizard - no weapon but can cast a spell for healing any injured warrior or archer on his side, health 10, strength 1

The screen will be splitted to 2 parts. Each part of the screen has the army and soldiers of the army are going to the center of the screen. When they meet the soldier of the other army they will fight. The result of the fight is a random number multiplied by strength and health of each soldier. In every turn, wizard of each side will heal random soldier who is injured. The wizard can be killed by enemy soldier.

At the end only one side can win the battle. Using switches we can set a number of soldier's kind for each side. For example we can set 5 wizards, 10 warriors and 10 archers for The White Race and 1 wizard, 20 warriors and 20 archers for The Black Race.

So what do you think?

[[User:Jirihradil|Jirihradil]] 20:09, 3 December 2012 (CET)

== Hive ==
'''author'''
:--[[User:Xseda07|Adam Sedláček (xseda07)]] 12:09, 30 November 2012 (CET)
<div>
As is known, the hive is a community that is very complex and is influenced by both internal and external factors. Therefore, I propose to create a simulation that would examine the influence of internal and external circumstances which influence the hive and the ecosystem in which they live. Especially I mean these factors:
<ul>
<li>Number and distance of flowers and fruit trees to pollinate</li>
<li> number of workers and drones in the hive
<li> how early beginning / end of summer / winter affect stocks of honey and colony survival
<li>how number of workers affect pollination of trees/ flowers and therefore the number of flowers and trees in neighbourhood
</ul>
<div>
'''How it will work'''
<div>
Workers are responsible for getting food for whole hive and also for pollination of trees and flowers. They are using sun for the orientation and they communicate between themselves. In the beehive there ale drones, which fertilizes Bee´s queen, bee´s queen, which oviposits and the eggs-larvas, which are later transformed to either workers or drones.
<div>
Trees/flowers need to be pollinated in order to proliferate. There will be also change of season and different hive behaviour during summer/winter
<div>
'''Method'''
I will use NetLogo to simulate the Hive
:OK, sounds interesting. '''Accepted'''. Please, identify yourself. [[User:Tomáš|Tomáš]] 22:49, 29 November 2012 (CET)
::I am sorry. --[[User:Xseda07|Adam Sedláček (xseda07)]] 12:09, 30 November 2012 (CET)

==To vote or not to vote? ==

'''author'''
:--[[User:Iuter88|Riccardo Torchio)]] 15:53, 3/12/2012 (CET)
<div>
I want to design a simulation that can show us how people decide if to go to vote or not.

I will create agent with
-proximity to a person that can influence the agent
-willingness to go to vote
-expected result of the vote
I can take my conclusion about the threshold value of this 3 variables in this process.
<div>
'''Method'''
i will use NetLogo to simulate the process

==Enter the market or not?==
I was thinking about a firms competition simulation. A first firm decides to enter the market or not and depending on the choice, the firm already in the market decides to fight or to accommodate the new firm. For example, I could take the example of fast-food in Belgium: the burger king chain could be trying to enter the market and thus the McDonald's chain already present could decide of its behavior.

Wagon Antoine
[[User:Qantw00|Qantw00]] 22:10, 3 December 2012 (CET)