Abstract
In this paper, the notion of equi-well-posed optimization problem as studied by Dontchev and Zolezzi, (Ref. 1) is extended to noncooperative games. Some existence theorems for Berge and Nash equilibria are obtained. Under some invariance properties, the existence of Berge equilibria which are also Nash equilibria points is studied.
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References
Dontchev, A. L., andZolezzi, T.,Well-Posed Optimization Problems, Springer Verlag, New York, New York, 1993.
Berge, C.,Théorie Générale des Jeux à n-Personnes, Gauthier-Villars, Paris, France, 1957.
Abalo, K. Y., andKostreva, M. M.,Fixed Points, Nash Games, and Their Organizations, Topological Methods in Nonlinear Analysis, Vol. 6, 1996.
Cavazzuti, E., andPacchiarotti, N.,Condizioni Sufficienti per la Dipendenza Continua dei Minimi da un Parametro, Bollettino della Unione Mathematica Italiana, Vol. 13B, pp. 261–279, 1976.
Arino, O., Gautier, S., andPenot, J. P.,A Fixed-Point Theorem for Sequentially Continuous Mappings with Applications to Ordinary Differential Equations, Funkcialaj Ekvacioj, Vol. 27, pp. 273–279, 1984.
Nash, J.,Noncooperative Games, Annals of Mathematics, Vol. 54, pp. 286–295, 1951.
Aubin, J. P.,Mathematical Methods of Games and Economic Theory, North Holland, Amsterdam, Holland, 1979.
Radjef, M. S.,Sur l'Existence d'un Equilibre de Berge pour un Jeu Différentiel à N-Personnes, Cahiers Mathématiques, Université d'Oran, Vol. 1, pp. 89–93, 1988.
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Communicated by F. Giannessi
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Abalo, K.Y., Kostreva, M.M. Equi-well-posed games. J Optim Theory Appl 89, 89–99 (1996). https://doi.org/10.1007/BF02192642
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DOI: https://doi.org/10.1007/BF02192642