Repeated games and partial differential equations
(1996) Mathematics of operations research — Vol. 21, n° 1, p. 209-236 (1996)
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- Let nu(n)(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 <epsilon(>)(p) = nu(n)(p) - cav(u)(p) is then converging to zero at least as rapidly as 1/root n. In this paper, we analyze the convergence of psi(n)(p) = root n epsilon(n)(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 psi* to a partial differential equation with appropriate boundary conditions and regularity properties implies the uniform convergence of psi(n) to the Fenchel conjugate of psi*. In particular cases, the P.D.E. problem is linear and its solution psi* is then related to the multidimensional normal distribution.
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Demeyer, B. (1996). Repeated games and partial differential equations. Mathematics of operations research, 21(1), 209-236. https://doi.org/10.1287/moor.21.1.209 (Original work published 1996)