Private Strategies in Repeated Games with Imperfect Public Monitoring
by
Steven A. Matthews
University of Pennsylvania
Coauthors: George J. Mailath (University of Pennsylvania), Tadashi Sekiguchi (University of Pennsylvania and Kobe University)

In a finitely repeated game with public monitoring, it is well-known that if the stage game equilibrium is unique, then the only perfect public equilibrium of the repeated game consists of playing the stage game equilibrium after any history. It is also known that replacing the public signal by a less informative statistic cannot expand, and generally shrinks, the set of perfect public equilibrium outcomes. We show that these results do not hold for the set of sequential equilibrium outcomes. That is, they are not generally true of sequential equilibria in which the strategies are private, i.e., depend on own past actions as well as the public signal. A key feature of some of the examples is that imperfect observability can help the administration of a sequentially rational punishment -- a deviator may be better punished if the other players are confused about who deviated. This phenomenon is unrelated to the "internal correlation" of strategies identified by previous authors.

Date received: June 12, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafi-50.