How Fast Do Equilibrium Payoff Sets Converge in Repeated Games?

We provide tight bounds on the rate of convergence of the equilibrium payo sets for repeated games under both perfect and imperfect public monitoring. The distance between the equilibrium payo set and its limit vanishes at rate (1− δ)1/2 under perfect monitoring, and at rate (1− δ)1/4 under imperfect monitoring. For strictly individually rational payo vectors, these rates improve to 0 (i.e., all strictly individually rational payo vectors are exactly achieved as equilibrium payo s for δ high enough) and (1− δ)1/2, respectively.

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