Approximate Solutions With Convergence Results for Optimal Control Problems Driven by Generalized Multiobjective Games With Application to Walrasian General Equilibrium

Abstract

The purpose of this paper is to establish convergence results of the approximate solutions for control systems of generalized multiobjective games and optimal control problems driven by generalized multiobjective games. First, we revisit the control systems of generalized multiobjective games. Then, using a sequence of ${\Gamma }^n$-converging mappings, we establish the upper convergence, lower convergence and convergence of the solution sets for such problems. Second, we investigate sufficient conditions for the convergence of approximate solutions to optimal control problems. Finally, as a real-world application, we consider the special case of control systems of economic equilibrium models. The results presented in the paper are new and improve some of the main results given in the literature.