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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. doman@emi.nw.ru
Victor Domansky
Affiliation:
Institute for Economics and Mathematics RAS, 1, Tchaikovsogo st., 191187, St.Petersburg, Russia. doman@emi.nw.ru
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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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References

R. Aumann and M. Maschler, Repeated Games with Incomplete Information. The MIT Press, Cambridge, Massachusetts, London, England (1995).
De Meyer, B., Price dynamics on a stock market with asymmetric information. Games Econ. Behav. 69 (2010) 42–71. Google Scholar
B. De Meyer and A. Marino, Continuous versus discrete market game. Cowles Foundation Discussion Paper (2005) 1535.
De Meyer, B. and Saley, H., On the Strategic Origin of Brownian Motion in Finance. Int. J. of Game Theory 31 (2002) 285–319. Google Scholar
Domansky, V., Repeated games with asymmetric information and random price fluctuations at finance markets. Int. J. Game Theory 36 (2007) 241–257. Google Scholar
Domansky, V., Symmetric representations of bivariate distributions. Statist. Prob. Lett. 83 (2013) 1054–1061. Google Scholar
Domansky, V. and Kreps, V., Repeated games with asymmetric information and random price fluctuations at finance markets. Proceedings of Applied and Industrial Mathematics 12 (2005) 950–952. Google Scholar
V. Domansky and V. Kreps, Repeated games with asymmetric information and random price fluctuations at finance markets: the case of countable state space. Centre d’Economie de la Sorbonne. Preprint 2009.40, Univ. Paris 1 (2009).
F. Gensbittel, Asymptotic analysis of repeated games with incomplete information. Thèse de doctorat de l’Université Paris 1, Panthéon-Sorbonne-Paris (10/12/2010), Bernard De Meyer (Dir). http:/tel.archives-ouvertes.fr/tel-00579522/fr/ (2010).
M.S. Sandomirskaia, On the estimates of the value of repeated game modeling biddings with bid-ask spread. Publications of the 3-d All-Russian Conference “The economic growth, resource-dependence and socio-economic disparity”, St. Petersburg (2012) 173–176.
Winkler, G., Extreme points of moment sets. Math. Oper. Res. 13 (1988) 581–587. Google Scholar