Two-Person Repeated Games with Finite Automata

Abraham Neyman & Daijiro Okada

We study two-person repeated games in which a player with a restricted set of strategies plays against an unrestricted player. An ex- ogenously given bound on the complexity of strategies, which is measured by the size of the smallest automata that implement them, gives rise to a restriction on strategies available to a player. We examine the asymptotic behavior of the set of equilibrium payoffs as the bound on the strategic complexity of the restricted player tends to infinity, but sufficiently slowly. Results from the study of zero sum case provide the individually rational payoff levels. In addition we will explicitly construct the punishment strategy of the unrestricted player with certain uniform properties.

May, 1998
Published in: 
International Journal of Game Theory 29 (2000), 309-325.