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Nash Equilibrium Computation in Subnetwork Zero-Sum Games With Switching Communications
Lou, Youcheng1,2; Hong, Yiguang2; Xie, Lihua3; Shi, Guodong4; Johansson, Karl Henrik5
AbstractIn 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 subgradient-based 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.
KeywordHeterogeneous stepsizes joint connection multi-agent systems Nash equilibrium weight-unbalanced graphs
Funding ProjectNNSF of China[71401163] ; NNSF of China[61333001] ; Hong Kong Scholars Program[XJ2015049] ; Beijing Natural Science Foundation[4152057] ; National Research Foundation of Singapore[NRF-CRP8-2011-03] ; Knut and Alice Wallenberg Foundation ; Swedish Research Council
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000385406100013
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Document Type期刊论文
Corresponding AuthorLou, Youcheng
Affiliation1.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Nanyang Technol Univ, Sch Elect & Elect Engn, Singapore 639798, Singapore
4.Australian Natl Univ, Coll Engn & Comp Sci, Canberra, ACT 0200, Australia
5.Royal Inst Technol, Sch Elect Engn, ACCESS Linnaeus Ctr, S-10044 Stockholm, Sweden
Recommended Citation
GB/T 7714
Lou, Youcheng,Hong, Yiguang,Xie, Lihua,et al. Nash Equilibrium Computation in Subnetwork Zero-Sum Games With Switching Communications[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2016,61(10):2920-2935.
APA Lou, Youcheng,Hong, Yiguang,Xie, Lihua,Shi, Guodong,&Johansson, Karl Henrik.(2016).Nash Equilibrium Computation in Subnetwork Zero-Sum Games With Switching Communications.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,61(10),2920-2935.
MLA Lou, Youcheng,et al."Nash Equilibrium Computation in Subnetwork Zero-Sum Games With Switching Communications".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 61.10(2016):2920-2935.
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