Abstract
In this paper, a Ky Fan inequality without compactness and semicontinuity assumptions is proved. The inequality is next applied in order to obtain existence results for Nash equilibrium points for two-person games in topological vector spaces and in reflexive Banach spaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
TAN, K. K., and YU, J., New Minimax Inequality with Applications to Existence Theorems of Equilibrium Points, Journal of Optimization Theory and Applications, Vol. 82, pp. 105–120, 1994.
WILLIAMS, R. J., Sufficient Conditions for Nash Equilibria in N-Person Games over Reflexive Banach Spaces, Journal of Optimization Theory and Applications, Vol. 30, pp. 383–394, 1980.
YU, J., On Nash Equilibria in N-Person Games over Reflexive Banach Spaces, Journal of Optimization Theory and Applications, Vol. 73, pp. 211–214, 1992.
CAVAZZUTI, E., An Extension of Nash's Theorem, Preprint, Dipartimento di Matematica Pura e Applicata, Università di Modena, Modena, Italy, 1996.
MOREAU, J. J., Inf-Convolutions, Sous-Additivé, Convexité des Fonctions Numériques, Journal de Mathématiques Pures et Appliquées, Vol. 49, pp. 109–154, 1970.
BORDER, K. C., Fixed-Points Theorems with Applications to Economics and Game Theory, Cambridge University Press, Cambridge, England, 1985.
YEN, C. L., A Minimax Inequality and Its Application to Variational Inequalities, Pacific Journal of Mathematics, Vol. 97, pp. 477–481, 1981.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lignola, M.B. Ky Fan Inequalities and Nash Equilibrium Points without Semicontinuity and Compactness. Journal of Optimization Theory and Applications 94, 137–145 (1997). https://doi.org/10.1023/A:1022611820107
Issue Date:
DOI: https://doi.org/10.1023/A:1022611820107