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Differential variational inequality approach to dynamic games with shared constraints. (English) Zbl 1302.91028

Summary: 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 \(\lambda\) and smoothing parameter \(\mu\) go to zero with the order \(\mu =o(\lambda )\). Numerical examples are given to illustrate the existence and convergence results.

MSC:

91A25 Dynamic games
49J40 Variational inequalities
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