SFB 303 Discussion Paper No. B-232

Author: Probst, Daniel A.
Title: Evolution, Automata and the Repeated Prisoners' Dilemma
Abstract: This paper introduces two ideas to the evolutionary analysis of the Abreu & Rubinstein automaton selection game (with complexity costs) for the repeated prisoners' dilemma. As a first point an evolutionary process with a constant influx of simple mutants is proposed. The second idea introduces an evolutionary stability concept for sets of automata. These sets consist of automata which are indistinguishable in an evolutionary process in terms of repeated game payoff and complexity. Stability of such a set requires every member to be evolutionary stable against all automata outside the set. The basic aim is to remedy the non-existence of ESS by allowing an equilibrium population to drift arbitrarily over a set while requiring that this drift will never allow the destabilization of the population by any mutants outside this set. It turns out that there exists one unique set of five three-state automata fulfilling the above requirements.
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Creation-Date: December 1992
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