Geodesic
Bidding games with several risky assets
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 6 (2014) no. 3, pp. 32-53.

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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 random prices depend on “a state of nature”, that is determined by the initial chance move according to a probability distribution that is known to both players. Player 1 (insider) is informed on the state of nature, but Player 2 is not. The bids may take any integer values. The $n$-stage model is reduced to a zero-sum repeated game with lack of information on one side of Player 2. 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. We give the solutions for corresponding infinite games. Analogously to the case of two risky assets (see [9]) the optimal strategy of Player 1 generates a random walk of transaction prices. The symmetry of this random walk is broken at the final stages of the game.
Keywords: bidding, repeated games, asymmetric information, optimal strategies, random walks. 
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Victor K. Domansky; Victoria L. Kreps. Bidding games with several risky assets. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 6 (2014) no. 3, pp. 32-53. http://geodesic.mathdoc.fr/item/MGTA_2014_6_3_a1/

[1] Domanskii V. K., Kreps V. L., “Moment obnaruzheniya “insaiderskoi” informatsii na torgakh s asimmetrichnoi informirovannostyu agentov”, Obozrenie prikladnoi i promyshlennoi matematiki, 14:3 (2007), 399–416

[2] Domanskii V. K., Kreps V. L., “Teoretiko-igrovaya model birzhevykh torgov: strategicheskie aspekty formirovaniya tsen na fondovykh rynkakh”, Zhurnal novoi ekonomicheskoi assotsiatsii, 2011, no. 11, 39–62

[3] Sandomirskaya M. S., “Tsena vnezapnogo raskrytiya insaiderskoi informatsii na fondovom rynke”, Vestnik Sankt-Peterburgskogo universiteta. Seriya 10, 2014, no. 1, 120–127

[4] Aumann R., Maschler M., Games with Incomplete Information, The MIT Press, Cambridge, Massachusetts–London, England, 1995 | MR | Zbl

[5] De Meyer B., Moussa Saley H., “On the Strategic Origin of Brownian Motion in Finance”, Int. Journal of Game Theory, 31 (2002), 285–319 | DOI | MR | Zbl

[6] De Meyer B., “Price dynamics on a stock market with asymmetric information”, Games and Economic Behavior, 69:1 (2010), 42–71 | DOI | MR | Zbl

[7] Domansky V., “Repeated games with asymmetric information and random price fluctuations at finance markets”, Int. J. Game Theory, 36:2 (2007), 241–257 | DOI | MR | Zbl

[8] Domansky V., “Symmetric representations of bivariate distributions”, Statistics and Probability Letters, 83 (2013), 1054–1061 | DOI | MR | Zbl

[9] Domansky V., Kreps V., “Repeated games with asymmetric information modeling financial markets with two risky assets”, RAIRO-Oper. Res., 47 (2013), 251–272 | DOI | MR | Zbl

[10] Kyle A. S., “Continuous auctions and insider trading”, Econometrica, 53 (1985), 1315–1335 | DOI | Zbl