# Pure equilibria in a simple dynamic model of strategic market game

Listed:
• Piotr Więcek

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## 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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File URL: http://hdl.handle.net/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. 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.
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### Keywords

Stochastic game; Constant-sum game; Pure stationary equilibrium; Finite strategy space; Strategic market game;

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