  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.
