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Repeated games with asymmetric information modeling financialmarkets with two risky assets∗

Published online by Cambridge University Press:  25 July 2013

Victoria Kreps  and
Victor Domansky
Victoria Kreps
Affiliation:
Institute for Economics and Mathematics RAS, 1, Tchaikovsogo st., 191187, St.Petersburg, Russia. [email protected]
Victor Domansky
Affiliation:
Institute for Economics and Mathematics RAS, 1, Tchaikovsogo st., 191187, St.Petersburg, Russia. [email protected]
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Abstract

We consider multistage bidding models where two types of risky assets (shares) are tradedbetween two agents that have different information on the liquidation prices of tradedassets. These prices are random integer variables that are determined by the initialchance move according to a probability distribution p over thetwo-dimensional integer lattice that is known to both players. Player 1 is informed on theprices of both types of shares, but Player 2 is not. The bids may take any integer values.The model of n-stage bidding is reduced to a zero-sum repeated game withlack of information on one side. We show that, if liquidation prices of shares have finitevariances, then the sequence of values of n-step games is bounded. This makes itreasonable to consider the bidding of unlimited duration that is reduced to the infinitegame G∞(p). We give the solutions for thesegames. Optimal strategies of Player 1 generate random walks of transaction prices. Butunlike the case of one-type assets, the symmetry of these random walks is broken at thefinal stages of the game.

Keywords

Multistage bidding modelrepeated gameasymmetric informationrandom walk
Type
Research Article
Information
RAIRO - Operations Research , Volume 47 , Issue 3 , July 2013 , pp. 251 - 272
Copyright
© EDP Sciences, ROADEF, SMAI, 2013

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