Evolution, Automata and Repeated Games

This paper further analyzes evolutionary stability in Abreu & Rubinstein automaton selection games, focusing primarily on the Repeated Prisoners'Dilemma and coordination games. We introduce a strengthening of the Binmore and Samuelson MESS concept called Evolutionary Stable Collections (ESC). While ESC exists uniquely in repeated coordination games, its nonexistence in the Prisoners' Dilemma case pinpoints an instability property of MESS. In a second step we assume that some types of mutants occur more often than others. For the specification that the least complex mutants occur frequently we show that in the Prisoners' Dilemma a perturbed version of ESC exists uniquely such that all evolutionary viable populations can only consist of five types of three-state automata which cooperate amongst themselves (and best-respond to the frequent mutants).