Simultaneous Social Cost Minimization and Nash Equilibrium Seeking in Non-cooperative Games
作者单位：School of Electrical and Electronic EngineeringNanyang Technological University
会议名称：《第36届中国控制会议》
会议届次：36
主办单位：Dalian University of Technology;Systems Engineering Society of China (SESC);Technical Committee on Control Theory (TCCT), Chinese Association of Automation (CAA)
会议日期：2017年
学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学]
基 金：supported by Singapore Economic Development Board under EIRP grant S14-1172-NRF EIRP-IHL
关 键 词：Nash equilibrium seeking social cost minimization interacting coalitions non-cooperative game
摘 要：An N-coalition non-cooperative game is formulated in this paper. In the considered game, there are N interacting coalitions and each of them includes a set of agents. Each coalition acts as a virtual player（VP） in the game that aims to minimize its own objective function, which is defined as the sum of the agents’ local objective functions in the coalition. However, the actual decision-makers are not the coalitions but the agents therein. That is, the agents within each coalition collaboratively minimize the coalition’s objective function while constituting an entity that serves as a self-interested player（i.e., the coalition）in the game among the interacting coalitions. A seeking strategy is designed for the agents to find the Nash equilibrium of the N-coalition non-cooperative games. The equilibrium seeking strategy is based on an adaptation of a dynamic average consensus protocol and the gradient play. The dynamic average consensus protocol is leveraged to estimate the averaged gradients of the coalitions’ objective functions. The gradient play is then implemented by utilizing the estimated information to achieve the Nash equilibrium seeking. Convergence results are established by utilizing Lyapunov stability analysis. A numerical example is given in supportive of the theoretical results.