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.
Hörner, Johannes and Takahashi, Satoru, "How Fast Do Equilibrium Payoff Sets Converge in Repeated Games?" (2016). Cowles Foundation Discussion Papers. 2473.