Bounded rationality,neural network and folk theorem in repeated games with discounting

Summary 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 7 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 paer 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.I would like to thank Hao Li and John Curran for excellent research assistance. Financial support from National Science Foundation (SES-9223483), Sloan Foundation and the Division of Social Sciences at the University of Chicago is gratefully acknowledged.