Equal Pay for all Prisoners / The Logic of Contrition

Boerlijst, M.C., Nowak, M.A., & Sigmund, K. (1997). Equal Pay for all Prisoners / The Logic of Contrition. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-97-073

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Abstract

This report deals with two questions concerning the emergence of cooperative strategies in repeated games. The first part is concerned with the Perfect Folk Theorem and presents a vast class of equilibrium solutions based on Markovian strategies. Simple strategies, called equalizers, are introduced and discussed: if players adopt such strategies, the same payoff results for every opponent. The second part analyzes strategies implemented by finite automata. Such strategies are relevant in an evolutionary context; an important instance is called Contrite Tit For Tat. In populations of players adopting such strategies, Contrite Tit For Tat survives very well -- at least as long as errors are restricted to mistakes in implementation ("the trembling hand"). However, this cooperative strategy cannot persist if mistakes in perception are included as well.

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