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Better-Reply Dynamics with Bounded Recall

Kyiv School of Economics, 03113 Kyiv, Ukraine
andriy{at}vms.huji.ac.il, http://www.gtcenter.org/people/andriy

A decision maker is engaged in a repeated interaction with Nature. The objective of the decision maker is to guarantee to himself the average payoff as large as the best-reply payoff 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 his recall and no matter what better-reply strategy he uses.

Key Words: better-reply dynamics; regret; bounded recall; fictitious play; approachability
History: Received: October 28, 2007; revision received: March 20, 2008;