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Continuous versus Discrete Market Games

Author

Listed:
  • Alexandre Marino

    (CERMSEM)

  • Bernard De Meyer

    (CERMSEM)

Abstract

De Meyer and Moussa Saley [4] provide an endogenous justification for the appearance of Brownian Motion in Finance by modeling the strategic interaction between two asymmetrically informed market makers with a zero-sum repeated game with one-sided information. The crucial point of this justification is the appearance of the normal distribution in the asymptotic behavior of Vn(P)//n. In De Meyer and Moussa Saley’s model [4], agents can fix a price in a continuous space. In the real world however, the market compels the agents to post prices in a discrete set. The previous remark raises the following question: Does the normal density still appear in the asymptotic of Vn//n for the discrete market game? The main topic of this paper is to prove that for all discretization of the price set, Vn(P)//n converges uniformly to 0. Despite of this fact, we do not reject De Meyer, Moussa analysis: when the size of the discretization step is small as compared to n-1/2, the continuous market game is a good approximation of the discrete one.

Suggested Citation

  • Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1535
    as

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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d15/d1535.pdf
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    References listed on IDEAS

    as
    1. DE MEYER , Bernard, 1993. "Repeated Games and the Central Limit Theorem," LIDAM Discussion Papers CORE 1993003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Victor Domansky, 2007. "Repeated games with asymmetric information and random price fluctuations at finance markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 241-257, October.
    2. De Meyer, Bernard, 2010. "Price dynamics on a stock market with asymmetric information," Games and Economic Behavior, Elsevier, vol. 69(1), pages 42-71, May.
    3. Bernard De Meyer, 2007. "Price Dynamics on a Stock Market with Asymmetric Information," Levine's Bibliography 321307000000000841, UCLA Department of Economics.
    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.
    5. Marina Sandomirskaia, 2017. "Repeated Bidding Games with Incomplete Information and Bounded Values: On the Exponential Speed of Convergence," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-7, March.

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