Finite memory and imperfect monitoring

In this paper, we consider a class of infinitely repeated games with imperfect public monitoring. We look at strongly 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≠Γ∞, but that Γk is a singleton. Moreover, this last result is essentially independent of the discount factor.