Differential variational inequality approach to dynamic games with shared constraints

• 成果类型: Article
• 署名作者: Chen, Xiaojun; Wang, Zhengyu
• 署名单位: Hong Kong Polytechnic University; Nanjing University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0689-1
• 发表日期: 2014
• 页码: 379-408
• 关键词: generalized Nash games; COMPLEMENTARITY; equilibrium; scheme

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.