Repeated Games with Forgetful Players∗

We present a model to investigate the behavior of forgetful players in infinitely repeated games. We assume that each player may forget the entire history of the play with a fixed probability. Our modeling specifications make a clear distinction between absentminded and forgetful players. We consider two extreme cases regarding the correlation of forgetfulness of the players. In the first case, forgetfulness is simultaneous: If a player forgets, so do the rest. For this part, we are able to prove two Folk theorems. In the other extreme, we consider the case where forgetfulness is independent between players, so players’ state of memory is no longer common knowledge. We focus on Conditionally Belief-Free strategies to recapture the recursive structure in the sense of Abreu, Pearce and Stacchetti (1986, 1990). By utilizing a method analogous to Ely, Horner and Olszewski (2005), we represent characterization results for the payoff set of conditionally belief-free strategies. ∗I owe special thanks to my advisor David Pearce for his valuable comments and suggestions at all stages of this project. I also thank the participants at Micro Student Workshop (2006, New York University), the 17 International Conference on Game Theory, (2006, Stony Brook), and 2006 South and South East Asia Econometric Society Meeting (Chennai, India). †Department of Economics, New York University, 19 W. 4 Street, 6 FL. New York, NY 10012 (e-mail: [email protected])