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

Games ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 100 ◽  
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.

scholarly journals Cooperation in the Finitely Repeated Prisoner’s Dilemma*

2017 ◽  
Vol 133 (1) ◽  
pp. 509-551 ◽  
Author(s):  
Matthew Embrey ◽  
Guillaume R Fréchette ◽  
Sevgi Yuksel
Keyword(s):  
Prisoner's Dilemma ◽  
Meta Analysis ◽  
Basin Of Attraction ◽  
Prisoner’S Dilemma ◽  
Repeated Game ◽  
Backward Induction ◽  
Repeated Prisoner’S Dilemma ◽  
The Subject ◽  
Repeated Prisoner's Dilemma

Abstract More than half a century after the first experiment on the finitely repeated prisoner’s dilemma, evidence on whether cooperation decreases with experience—as suggested by backward induction—remains inconclusive. This article provides a meta-analysis of prior experimental research and reports the results of a new experiment to elucidate how cooperation varies with the environment in this canonical game. We describe forces that affect initial play (formation of cooperation) and unraveling (breakdown of cooperation). First, contrary to the backward induction prediction, the parameters of the repeated game have a significant effect on initial cooperation. We identify how these parameters impact the value of cooperation—as captured by the size of the basin of attraction of always defect—to account for an important part of this effect. Second, despite these initial differences, the evolution of behavior is consistent with the unraveling logic of backward induction for all parameter combinations. Importantly, despite the seemingly contradictory results across studies, this article establishes a systematic pattern of behavior: subjects converge to use threshold strategies that conditionally cooperate until a threshold round; conditional on establishing cooperation, the first defection round moves earlier with experience. Simulation results generated from a learning model estimated at the subject level provide insights into the long-term dynamics and the forces that slow down the unraveling of cooperation.

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

2014 ◽  
Vol 24 (12) ◽  
pp. 1430035 ◽  
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.

scholarly journals Strategy Choice in the Infinitely Repeated Prisoner’s Dilemma

2019 ◽  
Vol 109 (11) ◽  
pp. 3929-3952 ◽  
Author(s):  
Pedro Dal Bó ◽  
Guillaume R. Fréchette
Keyword(s):  
Experimental Design ◽  
Statistical Methods ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Strategy Choice ◽  
Repeated Prisoner’S Dilemma ◽  
Tit For Tat ◽  
Perfect Monitoring ◽  
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)

scholarly journals The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence

2011 ◽  
Vol 101 (1) ◽  
pp. 411-429 ◽  
Author(s):  
Pedro Dal Bó ◽  
Guillaume R Fréchette
Keyword(s):  
Experimental Evidence ◽  
Repeated Games ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Evolution Of Cooperation ◽  
Risk Dominance ◽  
Repeated Prisoner’S Dilemma ◽  
Infinitely Repeated Games ◽  
Repeated Prisoner's Dilemma ◽  
Present Experimental Evidence

A usual criticism of the theory of infinitely repeated games is that it does not provide sharp predictions since there may be a multiplicity of equilibria. To address this issue, we present experimental evidence on the evolution of cooperation in infinitely repeated prisoner's dilemma games as subjects gain experience. We show that cooperation may prevail in infinitely repeated games, but the conditions under which this occurs are more stringent than the subgame perfect conditions usually considered or even a condition based on risk dominance. (JEL C71, C73)

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