Game-theoretic model of financial markets with two risky assets

Victor Domansky () and Victoria Kreps ()
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Victor Domansky: St.Petersburg Insitute for Economics and Mathematics, Russian Academy of Sciences (St.Petersburg, Russia). Leading researcher of the laboratory for Game Theory and Decision Making, St.Petersburg Institute for Economics and Mathematics RAS.
Victoria Kreps: St.Petersburg Institute for Economics and Mathematics, Russian Academy of Sciences (St.Petersburg, Russia). Leading researcher of the laboratory for Game Theory and Decision Making, St.Petersburg Institute for Economics and Mathematics RAS.

HSE Working papers from National Research University Higher School of Economics

Abstract: We consider multistage bidding models where two types of risky assets (shares) are traded between two agents that have different information on the liquidation prices of traded assets. These prices are random integer variables that are determined by the initial chance move according to a probability distribution p over the two-dimensional integer lattice that is known to both players. Player 1 is informed on the prices of both types of shares, but Player 2 is not. The bids may take any integer value. The model of n-stage bidding is reduced to a zero-sum repeated game with lack of information on one side. We show that, if liquidation prices of shares have finite variances, then the sequence of values of n-step games is bounded. This makes it reasonable to consider the bidding of unlimited duration that is reduced to the infinite game G1(p). We offer the solutions for these games. We begin with constructing solutions for these games with distributions p having twoand three-point supports. Next, we build the optimal strategies of Player 1 for bidding games G1(p) with arbitrary distributions p as convex combinations of his optimal strategies for such games with distributions having two- and three-point supports. To do this we construct the symmetric representation of probability distributions with fixed integer expectation vectors as a convex combination of distributions with not more than three-point supports and with the same expectation vectors.

Keywords: financial market; random walk of prices; asymmetric information; repeated game; optimal strategy; extreme points of convex sets. (search for similar items in EconPapers)
JEL-codes: C72 C73 D44 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2012
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Published in WP BRP Series: Economics / EC, July 2012, pages 1-28

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