Geodesic
Multistage Biddings with Risky Assets: the Case of Countable Set of Possible Liquidation Values
Contributions to game theory and management, Tome 1 (2007), pp. 92-106.

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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 modelling the biddings with countable sets of possible prices and admissible bids, unlike the above-mentioned paper, where two values of price are possible and arbitrary bids are allowed. It is shown that, if the liquidation price of a share has a finite dispersion, 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 dispersion 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.
Keywords: Multistage biddings, asymmetric information, repeated games, optimal strategy. 
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Victor Domansky; Victoria Kreps. Multistage Biddings with Risky Assets: the Case of Countable Set of Possible Liquidation Values. Contributions to game theory and management, Tome 1 (2007), pp. 92-106. http://geodesic.mathdoc.fr/item/CGTM_2007_1_a6/

[1] De Meyer B., Saley H., “On the Strategic Origin of Brownian Motion in Finance”, Int. J. of Game Theory, 31 (2002), 285–319 | DOI | MR | Zbl

[2] Aumann R., Maschler M., Repeated Games with Incomplete Information, The MIT Press, Cambridge–London, 1995 | MR | Zbl

[3] Domansky V., “Repeated games with asymmetric information and random price fluctuations at finance markets”, Int. J. of Game Theory, 36:2 (2007), 241–257 | DOI | MR | Zbl

[4] Domansky V., Kreps V., “Moment of revealing of insider information at biddings with asymmetric information of agents”, Proc. of Appl. and Indust. Math., 14:3 (2007), 399–416 (in Russian)