How Fast Do Equilibrium Payoff Sets Converge in Repeated Games?

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