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Games 2015, 6(3), 175-190; doi:10.3390/g6030175

What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma

Mathematics Department, The City College, 137 Street and Convent Avenue, New York City, NY 10031, USA
Academic Editors: Martin A. Nowak and Christian Hilbe
Received: 4 April 2015 / Revised: 1 June 2015 / Accepted: 8 June 2015 / Published: 25 June 2015
(This article belongs to the Special Issue Cooperation, Trust, and Reciprocity)
View Full-Text   |   Download PDF [210 KB, uploaded 25 June 2015]

Abstract

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. View Full-Text
Keywords: Prisoner’s Dilemma; stable cooperative behavior; iterated play; Markov strategies; good strategies, individual utility Prisoner’s Dilemma; stable cooperative behavior; iterated play; Markov strategies; good strategies, individual utility
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Akin, E. What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma. Games 2015, 6, 175-190.

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