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Stock market as a dynamic game with continuum of players

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  • Wiszniewska-Matyszkiel, Agnieszka

Abstract

This paper contains a game-theoretic model describing the behaviour of investors at a stock exchange. The model presented is developed to reect the actual market microstructure. The players constitute a non-uniform continuum, differing, among others, by the planning horizon, the external ow of money which can be invested, formation of expectations about future prices, which, briey, divides the investors into the following groups: fundamental analysts, chartist, users of various econometric models, users of Capital Asset Pricing Model, and players observing a random exogenous signal. Prices are determined by orders and the equilibrating mechanism of the stock exchange. The mechanism presented is the actual single-price auction system used, among others, at Warsaw Stock Exchange. One of the main issues are self-verifying beliefs. Results of numerical simulations of stock exchange based on the model are also included.

Suggested Citation

  • Wiszniewska-Matyszkiel, Agnieszka, 2005. "Stock market as a dynamic game with continuum of players," MPRA Paper 32982, University Library of Munich, Germany, revised 2006.
    • Handle: RePEc:pra:mprapa:32982
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    File URL: https://mpra.ub.uni-muenchen.de/32982/1/MPRA_paper_32982.pdf
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    References listed on IDEAS

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    1. Agnieszka Wiszniewska-Matyszkiel, 2002. "Discrete Time Dynamic Games With A Continuum Of Players I: Decomposable Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 331-342.
    2. Agnieszka Wiszniewska-Matyszkiel, 2003. "Discrete Time Dynamic Games With Continuum Of Players Ii: Semi-Decomposable Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 27-40.
    3. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    4. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
    5. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Balder, Erik J, 1995. "A Unifying Approach to Existence of Nash Equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 79-94.
    7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    8. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    10. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1994. "Construction of Stationary Markov Equilibria in a Strategic Market Game," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 975-1006, November.
    11. B. LeBaron, 2001. "A builder's guide to agent-based financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 254-261.
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    Citations

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    Cited by:

    1. Agnieszka Wiszniewska-Matyszkiel, 2016. "Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information," Annals of Operations Research, Springer, vol. 243(1), pages 147-177, August.
    2. Agnieszka Wiszniewska-Matyszkiel, 2014. "Open and Closed Loop Nash Equilibria in Games with a Continuum of Players," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 280-301, January.
    3. Agnieszka Wiszniewska-Matyszkiel, 2017. "Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 984-1007, March.

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    More about this item

    Keywords

    multistage games; continuum of players; Nash equilibrium; belief-distorted Nash equilibrium; stock exchange;
    All these keywords.

    JEL classification:

    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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