Approximations of Quasi-Equilibria and Nash Quasi-Equilibria in Terms of Variational Convergence

Abstract

Various types of variational convergence of functions and bifunctions are applied to study global approximations of a quasi-equilibrium problem and a Nash quasi-game (generalized noncooperative game), two typical and important optimization models. We prove that when the data of approximating problems of a problem under consideration converge in the sense of suitable types of epi-, epi/hypo-, lop-convergence, or their weak variants, approximate solutions of the above approximating problems set converge to solutions of the original problem. Some results are new and others improve certain known ones since the applied types of variational convergence are weaker than the usually used classical types.