Learning by Forgetful Players

Sjaak Hurkens

Abstract: A product set of pure strategies is said to be closed under best replies if all best replies against all possible mixtures of these strategies are contained in the set. Minimal sets with this property are called minimal curb sets. This paper presents a dynamic learning process that has two main characteristics: Players have a bounded memory and they play best replies against beliefs, formed on the basis of strategies used in the recent past. It is shown that this learning process leads the players to playing strategies from a minimal curb set. Several variations of the process are considered.

Keywords: Learning, curb sets.

Classification Numbers: C70, C72.

Games and Economic Behavior 11:304-329 (1995)