UNFORTUNATELY THSI LECTURE HAS BEEN CANCELLED.Technion - Israel Institute of Technology Department of Mathematics ===================================== PDE AND APPLIED MATHEMATICS SEMINAR ===================================== DATE: Tuesday, November 13, 2012 SPEAKER: Victoria Kreps, St.Petersburg Institute for Economics and Mathematics TITLE: Repeated games with asymmetric information modeling multistage bidding for risky assets ABSTRACT: We investigate a discrete variant of multistage bidding model for risky assets (shares) introduced by De Meyer and Moussa Saley (2002) to analyze the evolution of prices at finance markets with asymmetric information. Only integer prices and bids are admissible in contrast to De Meyer and Moussa Saley model. The zero-sum repeated games with incomplete information are considered modeling the bidding with countable sets of possible prices and bids. We show that, if the liquidation price of a share has a finite variance, then the sequence of total profits of Player 1 - the insider - in n-step games is bounded from above. This property distinguish the discrete model from the continuous De Meyer and Moussa Saley model and allows to consider the game with infinite number of steps without a beforehand given artificial restriction of the game duration. We construct explicitly the optimal strategies for this game. For constructing the optimal strategy of Player 1 (the insider) with arbitrary liquidation price of a share with finite variance we use the symmetric representation of distributions with fixed mean values as convex combinations of distributions with two-point supports and with the same mean values. The solutions for the games with two-point distributions was obtained in Domansky (2007). The optimal strategy of Player 1 generates a symmetric random walk of posterior expectations of liquidation price with absorption. The expected duration of this walk is equal to the initial variance of 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. The described results are contained in the preprint Domansky, Kreps (2009). References -------------- De Meyer, B., Saley H. (2002) On the Strategic Origin of Brownian Motion in Finance. Int. J. of Game Theory, 31, 285-319. Domansky, V. (2007) Repeated games with asymmetric information and random price fluctuations at finance markets. Int. J. of Game Theory, 36(2), 241-257. Domansky V., Kreps V. (2009)Repeated games with asymmetric information and random price fluctuations at finance markets: the case of countable state space. Centre d'Economie de la Sorbonne. Univ. Paris 1 , Pantheon - Sorbonne. Preprint 2009-40, MSE. <http://ces.univ-paris1.fr/cesdp/CESFramDP2009.htm> For further info: Itai Shafrir <shafrir@techunix.technion.ac.il> For past and future Applied Math/PDE seminars see: <http://www.math.technion.ac.il/pde/seminar.html> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Itai Shafrir <shafrir@math.technion.ac.il>