Finite memory and imperfect monitoring

In this paper, we consider a class of infinitely repeated games with imperfect public monitoring. We look at symmetric perfect public equilibria with memory K: equilibria in which strategies are restricted to depend only on the last K observations of public signals. Define ΓK to be the set of payoffs of equilibria with memory K. We show that for some parameter settings, ΓK = Γ∞ for sufficiently large K. However, for other parameter settings, we show that not only is limK→∞ ΓK 6= Γ∞, but that Γk is completely degenerate. Moreover, this last result is essentially independent of the discount factor. ∗We thank Stephen Morris, Steven Tadelis, and participants of the Yale Theory discussion group for comments and suggestions. The views expressed herein are the those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.