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Pure equilibria in a simple dynamic model of strategic market game

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  • Piotr Więcek

Abstract

We present a discrete model of two-person constant-sum dynamic strategic market game. We show that for every value of discount factor the game with discounted rewards possesses a pure stationary strategy equilibrium. Optimal strategies have some useful properties, such as Lipschitz property and symmetry. We also show value of the game to be nondecreasing both in state and discount factor. Further, for some values of discount factor, exact form of optimal strategies is found. For β less than $${2-\sqrt{2}}$$ , there is an equilibrium such that players make large bids. For β close to 1, there is an equilibrium with small bids. Similar result is obtained for the long run average reward game. Copyright Springer-Verlag 2009

Suggested Citation

  • Piotr Więcek, 2009. "Pure equilibria in a simple dynamic model of strategic market game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 59-79, March.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:1:p:59-79
    DOI: 10.1007/s00186-008-0210-4
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    References listed on IDEAS

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    1. Karatzas, Ioannis & Shubik, Martin & Sudderth, William D., 1997. "A strategic market game with secured lending," Journal of Mathematical Economics, Elsevier, vol. 28(2), pages 207-247, September.
    2. Bruce D. Craven & Sardar M. N. Islam, 2005. "Optimization in Economics and Finance," Dynamic Modeling and Econometrics in Economics and Finance, Springer, number 978-0-387-24280-4, June.
    3. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1992. "Construction of Stationary Markov Equilibria in a Strategic Market Game," Cowles Foundation Discussion Papers 1033, Cowles Foundation for Research in Economics, Yale University.
    4. Martin Shubik & Ward Whitt, 1973. "Fiat Money in an Economy with One Nondurable Good and No Credit (A Noncooperative Sequential Game)," Cowles Foundation Discussion Papers 355, Cowles Foundation for Research in Economics, Yale University.
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