The Structure of Nash Equilibrium in Repeated Games with Finite Automata

The authors study the Nash equilibria of a two-person, infinitely-repeated game in which players' preferences depend on repeated game payoffs and the complexity of the strategies they use. The model considered is that of A. Rubinstein (1986). Necessary conditions on the structure of the equilibria are derived. These results place significant restrictions on equilibrium payoffs. The results suggest that the introduction of implementation costs results in a striking discontinuity in the Nash equilibrium sets in terms of strategies and payoffs.