Forgiver triumphs in alternating prisoner's dilemma Journal Article

Author(s): Zagorsky, Benjamin M; Reiter, Johannes G; Chatterjee, Krishnendu; Nowak, Martin A
Article Title: Forgiver triumphs in alternating prisoner's dilemma
Affiliation IST Austria
Abstract: Cooperative behavior, where one individual incurs a cost to help another, is a wide spread phenomenon. Here we study direct reciprocity in the context of the alternating Prisoner's Dilemma. We consider all strategies that can be implemented by one and two-state automata. We calculate the payoff matrix of all pairwise encounters in the presence of noise. We explore deterministic selection dynamics with and without mutation. Using different error rates and payoff values, we observe convergence to a small number of distinct equilibria. Two of them are uncooperative strict Nash equilibria representing always-defect (ALLD) and Grim. The third equilibrium is mixed and represents a cooperative alliance of several strategies, dominated by a strategy which we call Forgiver. Forgiver cooperates whenever the opponent has cooperated; it defects once when the opponent has defected, but subsequently Forgiver attempts to re-establish cooperation even if the opponent has defected again. Forgiver is not an evolutionarily stable strategy, but the alliance, which it rules, is asymptotically stable. For a wide range of parameter values the most commonly observed outcome is convergence to the mixed equilibrium, dominated by Forgiver. Our results show that although forgiving might incur a short-term loss it can lead to a long-term gain. Forgiveness facilitates stable cooperation in the presence of exploitation and noise.
Journal Title: PLoS One
Volume: 8
Issue 12
ISSN: 1932-6203
Publisher: Public Library of Science  
Date Published: 2013-12-12
Start Page: Article number: e80814
Copyright Statement: This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. CC-BY
Sponsor: This work was supported by grants from the John Templeton Foundation, ERC Start grant (279307: Graph Games), FWF NFN Grant (No S11407N23 RiSE), FWF Grant (No P23499N23), and a Microsoft faculty fellows award.
DOI: 10.1371/journal.pone.0080814
Notes: We thank Sasha Rubin and Sebastian Novak for helpful comments and suggestions.
Open access: yes (OA journal)
IST Austria Authors
  1. Johannes Reiter
    12 Reiter
  2. Matthias Nowak
    15 Nowak