Preliminary Draft

This paper is a study of bounded memory in a reputation game. In particular, in a repeated cheap talk game with incomplete informa-tion on the sender’s type. The receiver is assumed to be constrained by a finite number of memory states and the memory rule is itself part of his strategy. The first result of this paper shows that in this reputation game the updating rule will be rather simple: monotonic and increasing. The second main result of this paper shows that when memory constraints are severe the updating rule will involve random-ization before reaching the extreme states. The key intuition is that in a two-player game with incomplete information randomization is used as a memory saving device and also as a strategic element: to test the opponent and give incentives for types to be revealed early in the game. The results in this paper extend to general reputation games where the normal type is a zero-sum player and the commitment type is playing a pure strategy