Let vn(p) denote the value of the n-times repeated zero-sum game with incomplete information on one side and full monitoring and let u(p) be the value of the average game G(p). The error term εn(p)=vn(p)–cav(u)(p) is then converging to zero at least rapidly as 1/√n. In this paper, we analyze the convergence of ψn(p)=√nεn(p) in the games with square payoff matrices such that the optimal strategy of the informed player in the average game G(p) is unique, is completely mixed and does not depend on p. Our main result is that the existence of a solution ψ* to a partial differential equation with appropriate boundary conditions and regularity properties implies the uniform convergence of ψn to the Fenchel conjugate of ψ*. In particular cases, the PDE problem is linear and its solution ψ* is then related to the multidimensional normal distribution.
