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Incomplete Information Games and the Normal Distribution

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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," CORE Discussion Papers 1995020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1995020
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    1. repec:spr:dyngam:v:8:y:2018:i:1:d:10.1007_s13235-017-0217-7 is not listed on IDEAS
    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. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications, Elsevier.
    4. 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.
    5. Fedor Sandomirskiy, 2016. "On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values," HSE Working papers WP BRP 148/EC/2016, National Research University Higher School of Economics.

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