Better-Reply Strategies with Bounded Recall

A decision maker (an agent) is engaged in a repeated interaction with Nature. The objective of the agent is to guarantee to himself the long-run average payoff as large as the best-reply payoff to Nature?s empirical distribution of play, no matter what Nature does. An agent 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: An agent 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.