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Variational Convergence of Bifunctions: Motivating Applications

It is shown that a number of variational and equilibrium problems can be cast as finding the maxinf-points or minsup-points of bivariate functions, for short, bifunctions. These problems include linear and nonlinear complementarity problems, fixed points, variational inequalities, inclusions, noncooperative games, and Walras and Nash equilibrium problems. One appeals to the theory of lopsided convergence for bifunctions to derive stability results for each one of these problems.