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Game-theoretic model of financial markets with two risky assets

Author

Listed:
  • 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.)

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.

Suggested Citation

  • Victor Domansky & Victoria Kreps, 2012. "Game-theoretic model of financial markets with two risky assets," HSE Working papers WP BRP 16/EC/2012, National Research University Higher School of Economics.
  • Handle: RePEc:hig:wpaper:16/ec/2012
    as

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    File URL: http://www.hse.ru/data/2012/07/04/1254134492/16EC2012.pdf
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    References listed on IDEAS

    as
    1. Jean-François Rouillard, 2017. "Credit Crunch and Downward Nominal Wage Rigidities," Cahiers de recherche 17-05, Departement d'économique de l'École de gestion à l'Université de Sherbrooke, revised Apr 2019.
    2. Andersson, Ake E., 1981. "Structural change and technological development," Regional Science and Urban Economics, Elsevier, vol. 11(3), pages 351-361, August.
    3. Bruni, V. & Rossi, E. & Vitulano, D., 2014. "Automated restoration of semi-transparent degradation via Lie groups and visibility laws," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 106(C), pages 109-123.
    4. Domansky, V. & Kreps, V., 2011. "Game Theoretic Bidding Model: Strategic Aspects of Price Formation at Stock Markets," Journal of the New Economic Association, New Economic Association, issue 11, pages 39-62.
    5. Victor Domansky, 2007. "Repeated games with asymmetric information and random price fluctuations at finance markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 241-257, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    financial market; random walk of prices; asymmetric information; repeated game; optimal strategy; extreme points of convex sets.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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