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Nash equilibrium computation in subnetwork zero-sum games with switching communications
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2016 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 61, no 10, 2920-2935 p., 7345550Article in journal (Refereed) Published
Abstract [en]

In this paper, we investigate a distributed Nash equilibrium computation problem for a time-varying multi-agent network consisting of two subnetworks, where the two subnetworks share the same objective function. We first propose a subgradientbased distributed algorithm with heterogeneous stepsizes to compute a Nash equilibrium of a zero-sum game. We then prove that the proposed algorithm can achieve a Nash equilibrium under uniformly jointly strongly connected (UJSC) weight-balanced digraphs with homogenous stepsizes. Moreover, we demonstrate that for weighted-unbalanced graphs a Nash equilibrium may not be achieved with homogenous stepsizes unless certain conditions on the objective function hold. We show that there always exist heterogeneous stepsizes for the proposed algorithm to guarantee that a Nash equilibrium can be achieved for UJSC digraphs. Finally, in two standard weight-unbalanced cases, we verify the convergence to a Nash equilibrium by adaptively updating the stepsizes along with the arc weights in the proposed algorithm. © 2015 IEEE.

Place, publisher, year, edition, pages
IEEE Press, 2016. Vol. 61, no 10, 2920-2935 p., 7345550
Keyword [en]
Heterogeneous stepsizes, Joint connection, Multiagent systems, Nash equilibrium, Weight-unbalanced graphs, Computation theory, Directed graphs, Distributed computer systems, Graph theory, Multi agent systems, Time varying networks, Joint connections, Multiagent networks, Nash equilibria, Nash equilibrium computations, Objective functions, Strongly connected, Game theory
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
URN: urn:nbn:se:kth:diva-194611DOI: 10.1109/TAC.2015.2504962ScopusID: 2-s2.0-84973543335OAI: diva2:1043897

Funding Details: Vetenskapsrådet. QC 20161101

Available from: 2016-11-01 Created: 2016-10-31 Last updated: 2016-11-02Bibliographically approved

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Johansson, Karl H.
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ACCESS Linnaeus Centre
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