Dear Editor,This letter is concerned with the distributed Nash equilibrium(NE)seeking in an N-player game over random graphs. We develop a distributed stochastic forward-backward(DSFB) algorithm based on local informa...Dear Editor,This letter is concerned with the distributed Nash equilibrium(NE)seeking in an N-player game over random graphs. We develop a distributed stochastic forward-backward(DSFB) algorithm based on local information exchange between agents. We prove that the DSFB algorithm can converge to an NE almost surely, and analyze the convergence rate of the proposed algorithm. Compared with the existing works on distributed NE seeking, the communication graph in this letter is supposed to be time-varying and stochastic, which makes the NE seeking algorithm more suitable for practical scenarios, but brings a great challenge in both the design and convergence analysis of the algorithm. Besides, by establishing a variational inequality on NE, we relax the co-coercivity or strong monotonicity assumption on the extended pseudo-gradient.展开更多
基金supported in part by the National Key R&D Program of China(2021ZD0112600)the National Natural Science Foundation of China(61873219,62103344,62173284)+2 种基金the Natural Science Foundation of Fujian Province of China(2021J01051)the Foundation of State Key Laboratory of Intelligent Control and Decision of Complex SystemsScience and Technology Projects of Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province(IKKEM)(HRTP-[2022]-25)。
文摘Dear Editor,This letter is concerned with the distributed Nash equilibrium(NE)seeking in an N-player game over random graphs. We develop a distributed stochastic forward-backward(DSFB) algorithm based on local information exchange between agents. We prove that the DSFB algorithm can converge to an NE almost surely, and analyze the convergence rate of the proposed algorithm. Compared with the existing works on distributed NE seeking, the communication graph in this letter is supposed to be time-varying and stochastic, which makes the NE seeking algorithm more suitable for practical scenarios, but brings a great challenge in both the design and convergence analysis of the algorithm. Besides, by establishing a variational inequality on NE, we relax the co-coercivity or strong monotonicity assumption on the extended pseudo-gradient.
