Strategy Choice in the Infinitely Repeated Prisoner’s Dilemma

We use a novel experimental design to reliably elicit subjects’ strategies in an infinitely repeated prisoner’s dilemma experiment with perfect monitoring. We find that three simple strategies repre‑ sent the majority of the chosen strategies: Always Defect, Tit‑for‑Tat, and Grim. In addition, we identify how the strategies systematically vary with the parameters of the game. Finally, we use the elicited strategies to test the ability to recover strategies using statistical methods based on observed round‑by‑round cooperation choices and find that this can be done fairly well, but only under certain conditions. (JEL C72, C73, C92)

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Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions

Games ◽

10.3390/g9040100 ◽

2018 ◽

Vol 9 (4) ◽

pp. 100 ◽

Cited By ~ 4

Author(s):

Shun Kurokawa ◽

Joe Yuichiro Wakano ◽

Yasuo Ihara

Keyword(s):

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Evolutionary Model ◽

Repeated Game ◽

Evolution Of Cooperation ◽

Fixation Probability ◽

Non Linear ◽

Repeated Prisoner’S Dilemma ◽

Tit For Tat ◽

Repeated Prisoner's Dilemma

Evolution of cooperation by reciprocity has been studied using two-player and n-player repeated prisoner’s dilemma games. An interesting feature specific to the n-player case is that players can vary in generosity, or how many defections they tolerate in a given round of a repeated game. Reciprocators are quicker to detect defectors to withdraw further cooperation when less generous, and better at maintaining a long-term cooperation in the presence of rare defectors when more generous. A previous analysis on a stochastic evolutionary model of the n-player repeated prisoner’s dilemma has shown that the fixation probability of a single reciprocator in a population of defectors can be maximized for a moderate level of generosity. However, the analysis is limited in that it considers only tit-for-tat-type reciprocators within the conventional linear payoff assumption. Here we extend the previous study by removing these limitations and show that, if the games are repeated sufficiently many times, considering non-tit-for-tat type strategies does not alter the previous results, while the introduction of non-linear payoffs sometimes does. In particular, under certain conditions, the fixation probability is maximized for a “paradoxical” strategy, which cooperates in the presence of fewer cooperating opponents than in other situations in which it defects.

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Limit Cycles Sparked by Mutation in the Repeated Prisoner's Dilemma

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414300353 ◽

2014 ◽

Vol 24 (12) ◽

pp. 1430035 ◽

Cited By ~ 8

Author(s):

Danielle F. P. Toupo ◽

David G. Rand ◽

Steven H. Strogatz

Keyword(s):

Limit Cycle ◽

Relative Abundance ◽

Limit Cycles ◽

Prisoner's Dilemma ◽

Prisoner’S Dilemma ◽

Homoclinic Bifurcations ◽

Repeated Prisoner’S Dilemma ◽

Tit For Tat ◽

Complexity Cost ◽

Repeated Prisoner's Dilemma

We explore a replicator–mutator model of the repeated Prisoner's Dilemma involving three strategies: always cooperate (ALLC), always defect (ALLD), and tit-for-tat (TFT). The dynamics resulting from single unidirectional mutations are considered, with detailed results presented for the mutations TFT → ALLC and ALLD → ALLC. For certain combinations of parameters, given by the mutation rate μ and the complexity cost c of playing tit-for-tat, we find that the population settles into limit cycle oscillations, with the relative abundance of ALLC, ALLD, and TFT cycling periodically. Surprisingly, these oscillations can occur for unidirectional mutations between any two strategies. In each case, the limit cycles are created and destroyed by supercritical Hopf and homoclinic bifurcations, organized by a Bogdanov–Takens bifurcation. Our results suggest that stable oscillations are a robust aspect of a world of ALLC, ALLD, and costly TFT; the existence of cycles does not depend on the details of assumptions of how mutation is implemented.

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