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Necessary and sufficient conditions for optimality in constrained general sum stochastic games

Yaji, Vinayaka G and Bhatnagar, Shalabh (2015) Necessary and sufficient conditions for optimality in constrained general sum stochastic games. In: SYSTEMS & CONTROL LETTERS, 85 . pp. 8-15.

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Official URL: http://dx.doi.org/10.1016/j.sysconle.2015.08.003 ...


In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. (C) 2015 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Keywords: Constrained Markov games; Stationary Nash equilibrium; Linear programs; Discounted and average cost/reward settings
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 10 Dec 2015 06:08
Last Modified: 10 Dec 2015 06:08
URI: http://eprints.iisc.ac.in/id/eprint/52881

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