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Repeated games with asymmetric information and random price fluctuations at finance markets: the case of countable state space

Author

Listed:
  • Victor C. Domansky

    (St. Petersburg Institute for Economics and Mathematics - Russian Academy of Sciences)

  • Victoria L. Kreps

    (St. Petersburg Institute for Economics and Mathematics - Russian Academy of Sciences)

Abstract

This paper is concerned with multistage bidding models introduced by De Meyer and Moussa Saley (2002) to analyze the evolution of the price system at finance markets with asymmetric information. The zero-sum repeated games with incomplete information are considered modeling the bidding with countable sets of possible prices and admissible bids. It is shown that, if the liquidation price of a share has a finite variance, then the sequence of values of n-step games is bounded and converges to the value of the game with infinite number of steps. We construct explicitly the optimal strategies for this game. The optimal strategy of Player 1 (the insider) generates a symmetric random walk of posterior mathematical expectations of liquidation price with absorption. The expected duration of this random walk is equal to the initial variance of liquidation price. The guaranteed total gain of Player 1 (the value of the game) is equal to this expected duration multiplied with the fixed gain per step

Suggested Citation

  • Victor C. Domansky & Victoria L. Kreps, 2009. "Repeated games with asymmetric information and random price fluctuations at finance markets: the case of countable state space," Documents de travail du Centre d'Economie de la Sorbonne 09040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised May 2009.
    • Handle: RePEc:mse:cesdoc:09040
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2009/09040.pdf
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    Cited by:

    1. Domansky, Victor, 2013. "Symmetric representations of bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1054-1061.
    2. 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.
    3. Domansky, V. & Kreps, V., 2011. "Game Theoretic Bidding Model: Strategic Aspects of Price Formation at Stock Markets," Journal of the New Economic Association, New Economic Association, issue 11, pages 39-62.

    More about this item

    Keywords

    Multistage bidding; asymmetric information; repeated games; optimal strategy;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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