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A Characterization of Stationary Nash Equilibria of Single Controller Constrained Stochastic Games

Author

Listed:
  • Vikas Vikram Singh

    (Industrial Engineering and Operations Research, IIT Bombay, Powai, Mumbai, 400076, India)

  • N. Hemachandra

    (Industrial Engineering and Operations Research, IIT Bombay, Powai, Mumbai, 400076, India)

Abstract

We consider a two player finite state-action general sum single controller constrained stochastic game with both discounted and average cost criteria. We consider the situation where player 1 has subscription-based constraints and player 2, who controls the transition probabilities, has realization-based constraints which can also depend on the strategies of player 1. It is known that a stationary Nash equilibrium for discounted case exists under strong Slater condition, while, for the average case, stationary Nash equilibrium exists if additionally the Markov chain is unichain. For each case we show that the set of stationary Nash equilibria of this game has one to one correspondence with the set of global minimizers of a certain nonconvex mathematical program. If the constraints of player 2 do not depend on the strategies of player 1, then the mathematical program reduces to a quadratic program. The known linear programs for zero sum games of this class can be obtained as a special case of above quadratic programs.

Suggested Citation

  • Vikas Vikram Singh & N. Hemachandra, 2015. "A Characterization of Stationary Nash Equilibria of Single Controller Constrained Stochastic Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-22.
    • Handle: RePEc:wsi:igtrxx:v:17:y:2015:i:02:n:s0219198915400186
    DOI: 10.1142/S0219198915400186
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    Keywords

    Constrained stochastic games; constrained Markov decision processes; occupation measure; single controller game; Nash equilibrium; mathematical program; 91A10; 91A15; 90C26; 90C20; 90C05;
    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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