Uniqueness and efficiency of Nash equilibrium in a family of randomly generated repeated games

Abstract

This paper describes the results of an analysis of the Nash equilibrium in randomly generated repeated games. We study two families of games: symmetric bimatrix games G( A, B) with B = A ⊤ and nonsymmetric bimatrix games (the first includes the classical games of prisoner dilemma, battle of the sexes, and chickens). We use pure strategies, implemented by automata of size two, and different strategy domination criteria. We observe that, in this environment, the uniqueness and efficiency of equilibria outcomes is the typical result.