Bounded Computational Capacity Equilibrium

TL;DR

This paper investigates how bounded computational power and memory costs influence equilibrium outcomes in repeated games, showing that as memory costs diminish, equilibrium payoffs approach the full set of feasible and rational payoffs.

Contribution

It establishes a folk theorem for repeated games with costly memory, contrasting previous results where memory was free, highlighting the importance of memory costs and mixing.

Findings

As memory cost approaches zero, equilibrium payoffs include all feasible and rational payoffs.

Memory costs significantly affect the set of equilibrium outcomes in bounded computational settings.

The result contrasts with prior work where free memory limited equilibrium payoffs.

Abstract

We study repeated games played by players with bounded computational power, where, in contrast to Abreu and Rubisntein (1988), the memory is costly. We prove a folk theorem: the limit set of equilibrium payoffs in mixed strategies, as the cost of memory goes to 0, includes the set of feasible and individually rational payoffs. This result stands in sharp contrast to Abreu and Rubisntein (1988), who proved that when memory is free, the set of equilibrium payoffs in repeated games played by players with bounded computational power is a strict subset of the set of feasible and individually rational payoffs. Our result emphasizes the role of memory cost and of mixing when players have bounded computational power.