Evolutionary stability in repeated games played by finite automata

Abstract

We consider a game in which "meta-players" choose finite automata to play a repeated stage game. Meta-players' utilities are lexicographic, first increasing in the (limit-of-the-means) payoffs of the repeated game and second decreasing in the number of states in their automaton. We examine the outcomes in this game which satisfy a version of evolutionary stability that has been modified to permit existence. We find that such automata must be efficient, in that they must maximize the sum of the (limit-of-the-means) payoffs from the repeated game.