SFB 303 Discussion Paper No. B-243

Author: Schlag, Karl H.
Title: Dynamic Stability in the Repeated Prisoners' Dilemma Played by Finite Automata
Abstract: We investigate the replicator dynamics of the repeated Prisoners' Dilemma played by finite automata. The players discount repeated game payoffs and incur a cost which is proportional to the number of states in the automaton they use. An initial result is that the singleton set that contains "Defect for Ever" is the only asymptotically stable set containing a pure strategy. We then search for asymptotically stable sets when the dynamics are restricted to initial distributions that contain some given types in their support. It is shown that "Tat for Tit" is the only pure strategy (up to look-a-likes) besides "Defect for Ever" that is contained in such a set when the discount factor is sufficiently close to one and the cost per state is arbitrarily small. "Tat for Tit" when playing against itself will defect first and then cooperate forever.
Keywords: replicator dynamic, tat for tit, evolution, repeated prisoners' dilemma, interior asymptotic stability
Creation-Date: December, 1993
URL: ../1993/b/bonnsfb243.pdf

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