Bidding Games with Several Risky Assets and Random Walks of Stock Market Prices

Authors

  • Victor Domansky St.Petersburg Institute for Econ. and Math. RAS
  • Victoria Kreps St.Petersburg Institute for Econ. and Math. RAS

Abstract

We consider multistage bidding models where several 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 Domansky and Kreps (2013)) 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:

multistage bidding, asymmetric information, price fluctuation, random walk, repeated game, optimal strategy

Downloads

Download data is not yet available.

References

Aumann, R. and M. Maschler (1995). Repeated Games with Incomplete Information. The MIT Press: Cambridge, Massachusetts - London, England.

De Meyer, B. (2010). Price dynamics on a stock market with asymmetric information. Games and Economic Behavior, 69(1), 42–71.

De Meyer, B. and A. Marino (2005). Continuous versus discrete market game. Cowles Foundation Discussion Paper , No 1535.

De Meyer, B. and H. Saley (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. (2013). Symmetric representations of bivariate distributions. Statistics and Probability Letters, 83, 1054–1061.

Domansky, V. and V. Kreps (2005). Repeated games with asymmetric information and random price fluctuations at finance markets. Proceedings of applied and industrial mathematics, 12(4), 950–952 (in Russian).

Domansky, V. and V. Kreps (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. Preprint 2009.40, Univ. Paris 1.

Domansky, V. and V. Kreps (2013). Repeated games with asymmetric information modeling financial markets with two risky assets. RAIRO-Oper. Res., 47, 251–272.

Domansky, V. and V. Kreps (2014). Bidding games with several risky assets. Mathematical game theory and its applications, 6(3), 32–54 (in Russian).

Gensbittel, F. (2010). 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/ .

Sandomirskaia, M. (2013 a). Sandomirskaia M. (2014) Game-theoretical dynamic insider trading model with non-zero bid-ask spread. Upravlenie bolshimi systemami (Large-scale Systems Control). Is. 49. 207–234 (in Russian).

Sandomirskaia, M. (2014 b). The price of sudden disclosure of inside information on stock market. Vestnik St. Petersburg University. Ser. 10. Is. 1, 120–127 (in Russian).

Downloads

Published

2022-05-24

How to Cite

Domansky, V., & Kreps, V. . (2022). Bidding Games with Several Risky Assets and Random Walks of Stock Market Prices. Contributions to Game Theory and Management, 8. Retrieved from https://gametheory.spbu.ru/article/view/13446

Issue

Vol. 8 (2015)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.