A Note on Equilibrium Problems with Properly Quasimonotone Bifunctions

Authors:
M. Bianchi;R. Pini
Affiliations:
Istituto di Econometria e Matematica per le Applicazioni Economiche, Finanziarie e Attuariali, Università Cattolica del Sacro Cuore, Largo Gemelli 1, 20123 Milano, Italy, (e-mail: mbi ...;Dipartimento di Metodi Quantitativi per l'Economia, Università degli Studi di Milano–Bicocca, Piazza dell'Ateneo Nuovo 1, 20126 Milano, Italy, (e-mail: rita.pini@unimib.it
Venue:
Journal of Global Optimization
Year:
2001

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Abstract

In this paper, we consider some well–known equilibrium problems and their duals in a topological Hausdorff vector space X for a bifunction F defined on \kk,where K is a convex subset of X. Some necessary conditions are investigated, proving different results depending on the behaviour of F on the diagonal set. The concept of proper quasimonotonicity for bifunctions is defined, and the relationship with generalized monotonicity is investigated. The main result proves that the condition of proper quasimonotonicity is sharp in order to solve the dual equilibrium problem on every convex set.