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Incomplete Information Games and the Normal Distribution

Author

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  • MERTENS, Jean-François

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • ZAMIR, Shmuel

    (The Hebrew University, Jerusalem, Israel)

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.

Suggested Citation

  • MERTENS, Jean-François & ZAMIR, Shmuel, 1995. "Incomplete Information Games and the Normal Distribution," LIDAM Discussion Papers CORE 1995020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1995020
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1995.html
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    Cited by:

    1. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Hadiza Moussa Saley & Bernard De Meyer, 2003. "On the strategic origin of Brownian motion in finance," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(2), pages 285-319.
    3. Fedor Sandomirskiy, 2014. "Repeated games of incomplete information with large sets of states," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 767-789, November.
    4. Fedor Sandomirskiy, 2018. "On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values," Dynamic Games and Applications, Springer, vol. 8(1), pages 180-198, March.

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