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

Vikas Vikram Singh () and N. Hemachandra ()
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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

International Game Theory Review (IGTR), 2015, vol. 17, issue 02, 1-22

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.

Keywords: Constrained stochastic games; constrained Markov decision processes; occupation measure; single controller game; Nash equilibrium; mathematical program; 91A10; 91A15; 90C26; 90C20; 90C05 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219198915400186

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