Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations

Abstract

We study the evolution of cooperation in the spatial prisoner's dilemma game, where besides unconditional cooperation and defection, tit-for-tat, win-stay-lose-shift and extortion are the five competing strategies. While pairwise imitation fails to sustain unconditional cooperation and extortion regardless of game parametrization, myopic updating gives rise to the coexistence of all five strategies if the temptation to defect is sufficiently large or if the degree distribution of the interaction network is heterogeneous. This counterintuitive evolutionary outcome emerges as a result of an unexpected chain of strategy invasions. Firstly, defectors emerge and coarsen spontaneously among players adopting win-stay-lose-shift. Secondly, extortioners and players adopting tit-for-tat emerge and spread via neutral drift among the emerged defectors. And lastly, among the extortioners, cooperators become viable too. These recurrent evolutionary invasions yield a five-strategy phase that is stable irrespective of the system size and the structure of the interaction network, and they reveal the most unexpected mechanism that stabilizes extortion and cooperation in an evolutionary setting.

7 two-column pages, 5 figures; accepted for publication in Scientific Reports [related work available at http://arxiv.org/abs/1401.8294]

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• Combination with anti-tit-for-tat remedies problems of tit-for-tat
• Mutation enhances cooperation in direct reciprocity
• Evolution of direct reciprocity in group-structured populations
• Grouping promotes both partnership and rivalry with long memory in direct reciprocity
• Conditions for the existence of zero-determinant strategies under observation errors in repeated games
• On the implementation of zero-determinant strategies in repeated games
• Properties of zero-determinant strategies in multichannel games
• Strategies that enforce linear payoff relationships under observation errors in Repeated Prisoner's Dilemma game