Incomplete Information Games and the Normal Distribution

Jean-François Mertens and Shmuel Zamir ()

No 1995020, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: We consider a repeated two-person zero-sum game in which the payoffs in the stage game are given by a 2 x 2 matrix. This is chosen (once) by chance, at the beginning of the game, to be either G1 or G2, with probabilities p and 1 - p respectively. The maximiser is informed of the actual payoff matrix chosen but the minimiser is not. Denote by vn(p) the value of the n -times repeated game (with the payoff function defined as the average payoff per stage), and by Voo (p) the value of the infinitely repeated game. It is proved that vn(p) = voo(p) + K(p) ( Ø(p) / [square root] n) + o ( 1/ [square root] n) where Ø(p) is an appropriately scaled normal distribution density function evaluated at its p -quantile, and the coefficient K (p) is either 0 or the absolute value of a linear function in p.

Date: 1995-03-01
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