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Existence of equilibrium pairs for free abstract economies. (English) Zbl 1199.91136
Summary: In this paper, using X. Wu’s existence theorem of maximal elements for lower semicontinuous correspondences [Proc. Am. Math. Soc. 125, No. 6, 1779–1783 (1997; Zbl 0871.47038)] and W. K. Kim and K. H. Lee’s existence theorems of best proximity pairs [J. Math. Anal. Appl. 316, No. 2, 433–446 (2006; Zbl 1101.47040)], we prove the existence of equilibrium pairs for free abstract economies first with upper semicontinuous and then with lower semicontinuous constraint correspondences and \(Q_\theta\)-majorized preference correspondences.

91B50 General equilibrium theory
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics