Finite automata play a repeated extensive game

This paper analyzes a two-player game in which each player has to choose an automaton (machine) which plays an infinitely repeated extensive game. We assume that the preferences of the player depend both on repeated game payoffs and the number of states of their machine. In contrast to repeated normal form games, it is shown that if the stage-game is an extensive game with perfect information, any Nash equilibrium of the machine game will induce a path consisting of a constant play of a Nash equilibrium of the stage-game. Journal of Economic Literature Classification number: C72.