Better-Reply Dynamics with Bounded Recall

A decision maker is engaged in a repeated interaction with Nature. The objective of the decision maker is to guarantee to himself the average payo¤ as large as the best-reply payo¤ to Nature’s empirical distribution of play, no matter what Nature does. The decision maker with perfect recall can achieve this objective by a simple better-reply strategy. In this paper we demonstrate that the relationship between perfect recall and bounded recall is not straightforward: The decision maker with bounded recall may fail to achieve this objective, no matter how long recall he has and no matter what better-reply strategy he employs. JEL classi…cation: C73; D81; D83 Keywords: Better-reply dynamics; regret; bounded recall; …ctitious play; approachability I thank Dean Foster, Sergiu Hart, Eilon Solan, Tymo…y Mylovanov, Peyton Young, participants of the seminars at the Hebrew University and Tel Aviv University for helpful discussions and suggestions. I am very grateful to an anonimous referee and an associate editor for valuable comments. This research was done while I was in the Center for Rationality, the Hebrew University, which is heartily thanked for its hospitality. I also gratefully acknowledge the …nancial support from Lady Davis and Golda Meir Fellowship Funds, the Hebrew University. y Kyiv School of Economics, 51 Dehtyarivska St., Suite 12, 03113 Kyiv, Ukraine. E-mail: [email protected]