UNFORTUNATELY THSI LECTURE HAS BEEN CANCELLED. 
 
 
Technion - Israel Institute of Technology
 
          Department of Mathematics
 
    =====================================
     PDE AND APPLIED MATHEMATICS SEMINAR
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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>
 
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