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A Result on Localization of Equilibria

Author

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  • M. Bianchi

    (Università Cattolica del Sacro Cuore)

  • R. Pini

    (Università di Milano-Bicocca)

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.

Suggested Citation

  • M. Bianchi & R. Pini, 2002. "A Result on Localization of Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 335-343, November.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:2:d:10.1023_a:1020888205598
    DOI: 10.1023/A:1020888205598
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    References listed on IDEAS

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    1. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
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    Cited by:

    1. L. J. Lin & W. P. Wan, 2004. "KKM Type Theorems and Coincidence Theorems with Applications to the Existence of Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 105-122, October.

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