This paper designs a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints.Due to the uncertainty of parameters in set constraints,the authors aim to find a gene...This paper designs a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints.Due to the uncertainty of parameters in set constraints,the authors aim to find a generalized Nash equilibrium in the worst case.However,it is challenging to obtain the exact equilibria directly because the parameters are from general convex sets,which may not have analytic expressions or are endowed with high-dimensional nonlinearities.To solve this problem,the authors first approximate parameter sets with inscribed polyhedrons,and transform the approximate problem in the worst case into an extended certain game with resource allocation constraints by robust optimization.Then the authors propose a distributed algorithm for this certain game and prove that an equilibrium obtained from the algorithm induces anε-generalized Nash equilibrium of the original game,followed by convergence analysis.Moreover,resorting to the metric spaces and the analysis on nonlinear perturbed systems,the authors estimate the approximation accuracy related toεand point out the factors influencing the accuracy ofε.展开更多
基金supported partly by the National Key R&D Program of China under Grant No.2018YFA0703800the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No.XDA27000000the National Natural Science Foundation of China under Grant Nos.61873262 and 61733018。
文摘This paper designs a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints.Due to the uncertainty of parameters in set constraints,the authors aim to find a generalized Nash equilibrium in the worst case.However,it is challenging to obtain the exact equilibria directly because the parameters are from general convex sets,which may not have analytic expressions or are endowed with high-dimensional nonlinearities.To solve this problem,the authors first approximate parameter sets with inscribed polyhedrons,and transform the approximate problem in the worst case into an extended certain game with resource allocation constraints by robust optimization.Then the authors propose a distributed algorithm for this certain game and prove that an equilibrium obtained from the algorithm induces anε-generalized Nash equilibrium of the original game,followed by convergence analysis.Moreover,resorting to the metric spaces and the analysis on nonlinear perturbed systems,the authors estimate the approximation accuracy related toεand point out the factors influencing the accuracy ofε.
