Differential variational inequality approach to dynamic games with shared constraints

Xiaojun Chen, Zhengyu Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

75 Citations (Scopus)


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 λ and smoothing parameter μ go to zero with the order μ = o (λ). Numerical examples are given to illustrate the existence and convergence results.
Original languageEnglish
Pages (from-to)379-408
Number of pages30
JournalMathematical Programming
Issue number1-2
Publication statusPublished - 1 Jan 2014


  • Dynamic game
  • Generalized Nash game
  • Monotone variational inequality
  • Regularization
  • Smoothing

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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