IDEAS home Printed from
   My bibliography  Save this paper

Incomplete Information Games and the Normal Distribution


  • MERTENS, Jean-François

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

  • ZAMIR, Shmuel

    (The Hebrew University, Jerusalem, Israel)


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

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Forges Francoise, 1994. "Posterior Efficiency," Games and Economic Behavior, Elsevier, vol. 6(2), pages 238-261, March.
    2. Ray, Indrajit, 1996. "Coalition-Proof Correlated Equilibrium: A Definition," Games and Economic Behavior, Elsevier, vol. 17(1), pages 56-79, November.
    3. Milgrom, Paul & Roberts, John, 1996. "Coalition-Proofness and Correlation with Arbitrary Communication Possibilities," Games and Economic Behavior, Elsevier, vol. 17(1), pages 113-128, November.
    4. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    5. Moreno, Diego & Wooders, John, 1996. "Coalition-Proof Equilibrium," Games and Economic Behavior, Elsevier, vol. 17(1), pages 80-112, November.
    6. Forges, Francoise, 1994. "A note on Pareto optimality in differential information economies," Economics Letters, Elsevier, vol. 46(1), pages 27-31, September.
    7. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    8. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    9. repec:dau:papers:123456789/182 is not listed on IDEAS
    10. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    11. Lehrer, Ehud & Sorin, Sylvain, 1997. "One-Shot Public Mediated Talk," Games and Economic Behavior, Elsevier, vol. 20(2), pages 131-148, August.
    12. d'Aspremont, Claude & Gerard-Varet, Louis-Andre, 1979. "Incentives and incomplete information," Journal of Public Economics, Elsevier, vol. 11(1), pages 25-45, February.
    13. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    14. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    15. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," CORE Discussion Papers 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    17. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    18. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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, 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.
    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.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cor:louvco:1995020. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alain GILLIS). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.