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A decentralized strategy for generalized Nash equilibrium with linear coupling constraints

Author

Listed:
  • Liu, Ping
  • Fu, Zao
  • Cao, Jinde
  • Wei, Yun
  • Guo, Jianhua
  • Huang, Wei

Abstract

In this paper, we proposed a continuous-time distributed algorithm based on the operator splitting method to search the generalized Nash equilibrium in non-cooperative game. For the considered problem, the local objective function of each player is effected by other players’ strategies within a local area network, meanwhile the local feasible strategy sets of players are coupled with each other over an undirected connected graph. The global linear inequality and equality constraints are employed to describe this relationship. With variational inequality theory, projection operator theory and Lyapunov stability theory, the convergence of the proposed decentralized algorithm is analyzed. Finally, a numerical example is formulated to verify the effectiveness of the proposed algorithm.

Suggested Citation

  • Liu, Ping & Fu, Zao & Cao, Jinde & Wei, Yun & Guo, Jianhua & Huang, Wei, 2020. "A decentralized strategy for generalized Nash equilibrium with linear coupling constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 221-232.
    • Handle: RePEc:eee:matcom:v:171:y:2020:i:c:p:221-232
    DOI: 10.1016/j.matcom.2019.06.004
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    References listed on IDEAS

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    1. Duda, Jozef, 2016. "A Lyapunov functional for a neutral system with a distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 171-181.
    2. Skjong, Stian & Pedersen, Eilif, 2019. "On the numerical stability in dynamical distributed simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 183-203.
    3. Koichi Nabetani & Paul Tseng & Masao Fukushima, 2011. "Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints," Computational Optimization and Applications, Springer, vol. 48(3), pages 423-452, April.
    4. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    5. Guo, Jianhua & Kong, Ye & Li, Zongzhi & Huang, Wei & Cao, Jinde & Wei, Yun, 2019. "A model and genetic algorithm for area-wide intersection signal optimization under user equilibrium traffic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 92-104.
    6. Guo, Jianhua & Liu, Yu & Li, Xiugang & Huang, Wei & Cao, Jinde & Wei, Yun, 2019. "Enhanced least square based dynamic OD matrix estimation using Radio Frequency Identification data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 27-40.
    7. Matsumoto, Akio & Szidarovszky, Ferenc, 2015. "Dynamic monopoly with multiple continuously distributed time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 99-118.
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