Bounded Rationality, Neural Network and Folk Theorem in Repeated Games with Discounting.

The perfect folk theorem (Fudenberg and Maskin, 1986) need not rely on excessively complex strategies. We recover the perfect folk theorem for two person repeated games with discounting through neural networks (Hopfield, 1982) that have finitely many associative units. For any individually rational payoff vector, we need neural networks with at most seven associative units, each of which can handle only elementary calculations such as maximum, minimum or threshold operation. The uniform upper bound of the complexity of equilibrium strategies differentiates this paper from Ben-Porath and Peleg (1987) in which we need to admit ever more complex strategies in order to expand the set of equilibrium outcomes.