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Contributed by William H. Press, April 19, 2012 (sent for review March 14, 2012)
Abstract
The two-player Iterated Prisoner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner’s Dilemma is an Ultimatum Game.
Footnotes
- ↵1To whom correspondence should be addressed. E-mail: wpress{at}cs.utexas.edu.
Author contributions: W.H.P. and F.J.D. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
Freely available online through the PNAS open access option.
- aDepartment of Computer Science and School of Biological Sciences, University of Texas at Austin, Austin, TX 78712; and
- bSchool of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540
Contributed by William H. Press, April 19, 2012 (sent for review March 14, 2012)
Abstract
The two-player Iterated Prisoner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner’s Dilemma is an Ultimatum Game.
- evolution of cooperation
- game theory
- tit for tat
Footnotes
- ↵1To whom correspondence should be addressed. E-mail: wpress{at}cs.utexas.edu.
Author contributions: W.H.P. and F.J.D. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
Freely available online through the PNAS open access option.
Iterated Prisoner's Dilemma strategies
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