Repeated games with asymmetric information and random price fluctuations at finance markets : the case of countable state space
AbstractThis 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.
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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 09040.
Length: 12 pages
Date of creation: Jan 2009
Date of revision: May 2009
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Multistage bidding; asymmetric information; repeated games; optimal strategy.;
Find related papers by 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 and Pricing - - - Auctions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-06-17 (All new papers)
- NEP-CTA-2009-06-17 (Contract Theory & Applications)
- NEP-GTH-2009-06-17 (Game Theory)
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- 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.
- Domansky, Victor, 2013. "Symmetric representations of bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1054-1061.
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