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Discrete Time Dynamic Games With Continuum Of Players Ii: Semi-Decomposable Games

Author

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  • AGNIESZKA WISZNIEWSKA-MATYSZKIEL

    (Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland;
    Institute of Computer Science, Polish Academy of Sciences, Poland)

Abstract

In this paper we consider dynamic games with continuum of players which can constitute a framework to model large financial markets. They are called semi-decomposable games.In semi-decomposable games the system changes in response to a (possibly distorted) aggregate of players' decisions and the payoff is a sum of discounted semi-instantaneous payoffs. The purpose of this paper is to present some simple properties and applications of these games. The main result is an equivalence between dynamic equilibria and families of static equilibria in the corresponding static perfect-foresight games, as well as between dynamic and static best response sets. The existence of a dynamic equilibrium is also proven. These results are counterintuitive since they differ from results that can be obtained in games with a finite number of players.The theoretical results are illustrated with examples describing large financial markets: markets for futures and stock exchanges.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:05:y:2003:i:01:n:s0219198903000866
    DOI: 10.1142/S0219198903000866
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    Citations

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    Cited by:

    1. 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.
    2. Jian Yang, 2021. "Analysis of Markovian Competitive Situations Using Nonatomic Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 184-216, March.
    3. Wiszniewska-Matyszkiel, Agnieszka, 2005. "Stock market as a dynamic game with continuum of players," MPRA Paper 32982, University Library of Munich, Germany, revised 2006.

    More about this item

    Keywords

    Dynamic game; discrete time; continuum of players; equilibrium; financial markets; 91AD10; 91A13; 91A40; 91A50; 91A80;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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