Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/19616
Title: Differential variational inequality approach to dynamic games with shared constraints
Authors: Chen, X 
Wang, Z
Keywords: Dynamic game
Generalized Nash game
Monotone variational inequality
Regularization
Smoothing
Issue Date: 2014
Publisher: Springer Verlag
Source: Mathematical programming, 2014, v. 146, no. 1-2, p. 379-408 How to cite?
Journal: Mathematical Programming 
Abstract: 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.
URI: http://hdl.handle.net/10397/19616
ISSN: 0025-5610
DOI: 10.1007/s10107-013-0689-1
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