Lindgren, Kristian and Verendel, Vilhelm (2013): Evolutionary Exploration of the Finitely Repeated Prisoners' DilemmaThe Effect of OutofEquilibrium Play. Published in: Games , Vol. 4, No. 1 : pp. 120.

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Abstract
The finitely repeated Prisoners' Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a gametheoretic analysis and the behaviour often observed among human players, where cooperation is maintained through most of the game. A gametheoretic reasoning based on backward induction eliminates strategies step by step until defection from the first round is the only remaining choice, reflecting the Nash equilibrium of the game. We investigate the Nash equilibrium solution for two different sets of strategies in an evolutionary context, using replicatormutation dynamics. The first set consists of conditional cooperators, up to a certain round, while the second set in addition to these contains two strategy types that react differently on the first round action: The "Convincer" strategies insist with two rounds of initial cooperation, trying to establish more cooperative play in the game, while the "Follower" strategies, although being first round defectors, have the capability to respond to an invite in the first round. For both of these strategy sets, iterated elimination of strategies shows that the only Nash equilibria are given by defection from the first round. We show that the evolutionary dynamics of the first set is always characterised by a stable fixed point, corresponding to the Nash equilibrium, if the mutation rate is sufficiently small (but still positive). The second strategy set is numerically investigated, and we find that there are regions of parameter space where fixed points become unstable and the dynamics exhibits cycles of different strategy compositions. The results indicate that, even in the limit of very small mutation rate, the replicatormutation dynamics does not necessarily bring the system with Convincers and Followers to the fixed point corresponding to the Nash equilibrium of the game. We also perform a detailed analysis of how the evolutionary behaviour depends on payoffs, game length, and mutation rate.
Item Type:  MPRA Paper 

Original Title:  Evolutionary Exploration of the Finitely Repeated Prisoners' DilemmaThe Effect of OutofEquilibrium Play 
Language:  English 
Keywords:  backward induction; rationality; prisoners' dilemma; evolutionary dynamics 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  43662 
Depositing User:  Vilhelm Verendel 
Date Deposited:  09 Jan 2013 08:45 
Last Modified:  11 May 2019 14:37 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/43662 