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General-sum stochastic games: Verifiability conditions for Nash equilibria

Prasad, HL and Bhatnagar, S (2012) General-sum stochastic games: Verifiability conditions for Nash equilibria. In: AUTOMATICA, 48 (11). pp. 2923-2930.

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Official URL: http://dx.doi.org/10.1016/j.automatica.2012.06.088


Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair. (c) 2012 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to PERGAMON-ELSEVIER SCIENCE LTD, ENGLAND
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Francis Jayakanth
Date Deposited: 31 Dec 2012 05:15
Last Modified: 31 Dec 2012 05:15
URI: http://eprints.iisc.ac.in/id/eprint/45470

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