Differential variational inequality approach to dynamic games with shared constraints

被引:98
作者
Chen, Xiaojun [1 ]
Wang, Zhengyu [2 ]
机构
[1] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China
[2] Nanjing Univ, Dept Math, Nanjing 210008, Jiangsu, Peoples R China
基金
中国国家自然科学基金;
关键词
Generalized Nash game; Dynamic game; Monotone variational inequality; Smoothing; Regularization; GENERALIZED NASH GAMES; COMPLEMENTARITY; EQUILIBRIUM; SCHEME;
D O I
10.1007/s10107-013-0689-1
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
The dynamic Nash equilibrium problem with shared constraints (NEPSC) involves a dynamic decision process with multiple players, where not only the players' cost functionals but also their admissible control sets depend on the rivals' decision variables through shared constraints. For a class of the dynamic NEPSC, we propose a differential variational inequality formulation. Using this formulation, we show the existence of solutions of the dynamic NEPSC, and develop a regularized smoothing method to find a solution of it. We prove that the regularized smoothing method converges to the least norm solution of the differential variational inequality, which is a solution of the dynamic NEPSC as the regularization parameter and smoothing parameter go to zero with the order . Numerical examples are given to illustrate the existence and convergence results.
引用
收藏
页码:379 / 408
页数:30
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