N-Player prisoners dilema - Revision history

Xhudj17: /* References */

2016-01-31T22:18:02Z

‎References

Xhudj17: /* Coalitions */

2016-01-31T22:14:47Z

‎Coalitions

Xhudj17: /* Communication/Visibility */

2016-01-31T22:05:16Z

‎Communication/Visibility

Xhudj17: /* construct */

2016-01-31T21:54:25Z

‎construct

Xhudj17: /* Problem explanation */

2016-01-31T21:54:11Z

‎Problem explanation

Xhudj17: /* Coalitions */

2016-01-31T21:53:57Z

‎Coalitions

Xhudj17: /* Environment */

2016-01-31T21:53:33Z

‎Environment

Xhudj17: /* Iteration */

2016-01-31T21:51:48Z

‎Iteration

Xhudj17: /* Coalitions */

2016-01-31T21:50:08Z

‎Coalitions

Xhudj17: /* Problem explanation */

2016-01-31T21:48:08Z

‎Problem explanation

← Older revision		Revision as of 22:18, 31 January 2016
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	==References==		==References==
	<references/>		<references/>
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		+	==See also==
		+	Prisoner's dilemma (czech version) http://www.simulace.info/index.php/Prisoner%27s_dilemma/cs

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 <div>That means, s*-1 is the minimum number of other cooperators which will secure that if the player will cooperate, he will get better profit than when all of them will defect. </div>
 <div style="text-align: center;"> [[File:GraphNPD1.png]] </div>
-<div>This number is really important when we are thinking about situation, where players can form coalitions. Let’s return to our example. Imagine that one of the companiesAlpha is making decision about the advertisement. The situation is following: One company did buy the advertisement and it is making 260 crowns. The others including Alpha are making 175. The companies, that have no advertisement, formed coalition and they want not to advertise. They asked Alpha to join them.
+<div>This number is really important when we are thinking about situation, where players can form coalitions. Let’s return to our example. Imagine that one of the companies (Alpha) is making decision about the advertisement. The situation is following: One company did buy the advertisement and it is making 260 crowns. The others including Alpha are making 175. The companies, that have no advertisement, formed coalition and they want not to advertise. They asked Alpha to join them.
 {| class="wikitable"
 |-

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 *if the player knows the previous decisions of others
 ===Communication/Visibility===
-There are several possibilities, how and if the players can communicate or see each other’s previous decisions. If there is no visibility, the players have to guess the moves of others. Of course, if they know the payoff curves, they can even count the previous moves out of their profit. Other possibility is for example to see neighbors only, random agents, fixed positions or everybody. This visibility, knowledge of previous moves, is crucial for some types of strategies and for creating and respecting the agreements or coalitions. From some studies (pridatstudie) we can see that rate of cooperation is rising with more visibility, but too much links can have opposite effect.
+There are several possibilities, how and if the players can communicate or see each other’s previous decisions. If there is no visibility, the players have to guess the moves of others. Of course, if they know the payoff curves, they can even count the previous moves out of their profit. Other possibility is for example to see neighbors only, random agents, fixed positions or everybody. This visibility, knowledge of previous moves, is crucial for some types of strategies and for creating and respecting the agreements or coalitions.
 ===Coalitions===
 To show some how the coalitions can work, let’s make few assumptions.Let N = {1,2,3,.....,n} be our set of players. Each of them has an option to defect (D) or cooperate (C). Also let h to be number of other cooperators. (number of cooperators not including the decision-making player)

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 ===Nature===
 The next example we can find between animals. There are lots of species that are living in groups and also lots of others, living separately. The dilemma is to cooperate, be a part of a pack and share your food, space and so on, or to be on your own, more vulnerable, with risk of not finding any food at all.
 ==References==
 <references/>

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 As we can see, the advertise (defect) option is always better for the individual company, but the more companies defect, the more money is lost from the market.
 Unfortunately, this is just the beginning. Here are some questions that we can ask about this situation:
-<ref name="An Investigation of N-person Prisoners’ Dilemmas"> An Investigation of N-person Prisoners’ Dilemmas Miklos N. Szilagyi http://www.complex-systems.com/pdf/14-2-3.pdf  2015-01-20</ref>
+<ref name="An Investigation of N-person Prisoners’ Dilemmas"> An Investigation of N-person Prisoners’ Dilemmas Miklos N. Szilagyi http://www.complex-systems.com/pdf/14-2-3.pdf  2016-01-20</ref>
 *Are the choices and actions of the agents simultaneous or distributed in time?
 *Can individual agents see and adapt to the actions of others?

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 <math display="inline">f(C,s^*-2) < f(D,0) \le f(C,s^*-1)</math>
 <ref> The Possibility of Cooperation in an N-Person Prisoners' Dilemma with Institutional
-Arrangements Akira Okada http://www.vse-lee.cz/app/webroot/files/useruploads/arno_riedl/okada(possibilitycooperationnpersonprisonersdilemmainstitutionalarrangements)puch93.pdf 2015-01-22</ref>
+Arrangements Akira Okada http://www.vse-lee.cz/app/webroot/files/useruploads/arno_riedl/okada(possibilitycooperationnpersonprisonersdilemmainstitutionalarrangements)puch93.pdf 2016-01-22</ref>
 <div>That means, s*-1 is the minimum number of other cooperators which will secure that if the player will cooperate, he will get better profit than when all of them will defect. </div>
 <div style="text-align: center;"> [[File:GraphNPD1.png]] </div>

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 Imagine 5 companies again producing the same product and polluting one lake in one town. They know that if they won’t stop polluting the water, the town will lose all citizens and they will go bankrupt. But the clearing of their waste costs money and raises prices of their product. Hence the company that will clear its waste will probably go bankrupt even faster. So there is a high chance, that all of them will pollute.
-Fortunately, situations like this are solved by long term agreements or restrictions. Agreements are based on the long term view. When even one of the companies won’t cooperate, the citizens will move and they all will go bankrupt, so the only rational choice is to cooperate. The restrictions are designed to change the payoff curves in such way, that defect option is way worse, than cooperating.
+Fortunately, situations like this are solved by long term agreements or restrictions. Agreements are based on the long term view. When even one of the companies won’t cooperate, the citizens will move and they all will go bankrupt, so the only rational choice is to cooperate. The restrictions are designed to change the payoff curves in such way, that defect option is way worse, than cooperating.<ref> The Environmental Prisoners’ Dilemma Eric K. Clemons
 ===Nature===

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 Iterated games are much more complex than single-shot games. Players will react to the previous decisions and to the changing situation. There is also a difference, if the game has given end and if the players know how much rounds are left.
 <div>
-There was a tournament of different strategies in iterated n-person prisoner’s dilemma organized by Robert Axelrod. The players had to choose a strategy and then stick to it. The tournament was done by an algorithm in which the different strategies were entered. The winning strategy was “tit for tat”. It was very simple, cooperate in the first turn and then do whatever the opponents will. This was done for the 2 player version, but we can use this strategy even in N-player game. The difference will be, that the player has to have a “tolerance level”, that is the minimal number of defectors, which will trigger the defect reaction.
+There was a tournament of different strategies in iterated n-person prisoner’s dilemma organized by Robert Axelrod<ref>Axelrod, Robert (1984), The Evolution of Cooperation, Basic Books, ISBN 0-465-02122-0</ref>. The players had to choose a strategy and then stick to it. The tournament was done by an algorithm in which the different strategies were entered. The winning strategy was “tit for tat”. It was very simple, cooperate in the first turn and then do whatever the opponents will. This was done for the 2 player version, but we can use this strategy even in N-player game. The difference will be, that the player has to have a “tolerance level”, that is the minimal number of defectors, which will trigger the defect reaction.
 ===Personalities===