A Result on Localization of Equilibria

M. Bianchi and R. Pini
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M. Bianchi: Università Cattolica del Sacro Cuore
R. Pini: Università di Milano-Bicocca

Journal of Optimization Theory and Applications, 2002, vol. 115, issue 2, No 5, 335-343

Abstract: Abstract In this paper, we deal with a general equilibrium problem where a bimap F: A×B ⊑ X×Y→2 Z is involved. This problem contains the scalar equilibrium problem as a very special case. The general equilibrium is considered via the properties of the map G: B→2 A naturally associated to the problem. The main result shows that, to have solutions on every convex subsets B 1 of B, localized via a map T: B→2 A , a necessary and sufficient condition is the KKM property of the map G with respect to T. The assumptions require that T satisfies a regularity condition with respect to G, and it is proved that this condition is quite sharp, providing a suitable counterexample.

Keywords: KKM maps; equilibrium problems for bimaps; proper quasimonotone bimaps (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1020888205598

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