Bounded Memory with Finite Action Spaces ∗ Mehmet Barlo Sabancı University Guilherme Carmona Universidade Nova de Lisboa Hamid Sabourian University of Cambridge June 16, 2009 Abstract We show that the Folk Theorem holds for any 2 player repeated game with (time- independent) limited-memory pure strategies, and with discounting. That is, we prove that any strictly individually rational payoff can be approximated with a limited- memory strict subgame perfect strategy profile (involving only pure actions) when players are sufficiently patient. The same argument used to establish this result can be used to prove a Nash-threat Folk Theorem in bounded memory strict SPE for n – players games. Furthermore, we show that, if there is a vector of confusion-proof minmax actions, then the Folk Theorem holds for full dimensional n – person games in bounded memory strict SPE. Journal of Economic Literature Classification Numbers: C72; C73; C79 Keywords: Repeated Games; Memory; Bounded Rationality; Folk Theorem * We wish to thank George Mailath and Wojciech Olszewski for very helpful suggestions. Any remaining errors are, of course, ours. 1