What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma
For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-06-01
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| Series: | Games |
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| Online Access: | http://www.mdpi.com/2073-4336/6/3/175 |
| _version_ | 1818554279838875648 |
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| author | Ethan Akin |
| author_facet | Ethan Akin |
| author_sort | Ethan Akin |
| collection | DOAJ |
| description | For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from the so-called Folk Theorem for supergames, and the proof constructs an explicit memory-one example, which has been labeled Grim. Here we describe all the memory-one good strategies for the non-symmetric version of the Prisoner’s Dilemma. This is the natural object of study when the payoffs are in units of the separate players’ utilities. We discuss the special advantages and problems associated with some specific good strategies. |
| first_indexed | 2024-12-12T09:37:17Z |
| format | Article |
| id | doaj.art-b79371a6aa1c42b1af0e68a1fcba297a |
| institution | Directory Open Access Journal |
| issn | 2073-4336 |
| language | English |
| last_indexed | 2024-12-12T09:37:17Z |
| publishDate | 2015-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Games |
| spelling | doaj.art-b79371a6aa1c42b1af0e68a1fcba297a2022-12-22T00:28:42ZengMDPI AGGames2073-43362015-06-016317519010.3390/g6030175g6030175What You Gotta Know to Play Good in the Iterated Prisoner’s DilemmaEthan Akin0Mathematics Department, The City College, 137 Street and Convent Avenue, New York City, NY 10031, USAFor the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from the so-called Folk Theorem for supergames, and the proof constructs an explicit memory-one example, which has been labeled Grim. Here we describe all the memory-one good strategies for the non-symmetric version of the Prisoner’s Dilemma. This is the natural object of study when the payoffs are in units of the separate players’ utilities. We discuss the special advantages and problems associated with some specific good strategies.http://www.mdpi.com/2073-4336/6/3/175Prisoner’s Dilemmastable cooperative behavioriterated playMarkov strategiesgood strategies, individual utility |
| spellingShingle | Ethan Akin What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma Games Prisoner’s Dilemma stable cooperative behavior iterated play Markov strategies good strategies, individual utility |
| title | What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma |
| title_full | What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma |
| title_fullStr | What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma |
| title_full_unstemmed | What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma |
| title_short | What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma |
| title_sort | what you gotta know to play good in the iterated prisoner s dilemma |
| topic | Prisoner’s Dilemma stable cooperative behavior iterated play Markov strategies good strategies, individual utility |
| url | http://www.mdpi.com/2073-4336/6/3/175 |
| work_keys_str_mv | AT ethanakin whatyougottaknowtoplaygoodintheiteratedprisonersdilemma |