Abstract
In this paper, by using a minimax inequality obtained by the author, some existence theorems of Pareto equilibria for multicriteria games without compactness, continuity and concavity are proved in topological vector spaces and 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
R. J., Williams, Sufficient conditions for Nash equilibria in N-person games over reflexive Banach spaces, J. Optim. Theory and Appl., 30 (1980), 383–394.
J., Yu, On nash equilibria in N-person games over reflexive Banach spaces, J. Optim. Theory and Appl., 73 (1992), 211–214.
J. C., Yao, Nash equilibria in N-person games with convexity, Appl. Math. Lett., 5, 5 (1992), 67–69.
K. K., Tan and J., Yu, New minimax inequality with applications to existence theorems of equilibrium points. J. Optim. Theory and Appl., 82 (1994), 105–120.
D., Ghose and U. R., Prasad, Solution concepts in two-person multicriteria games, J. Optim. Theory and Appl., 63 (1989), 167–189.
F., Szidarovszky, M. E., Gershou and L., Duckstein, Techniques for Multiobjective Decision Making in Systems Management, Elsevier, Amsterdam (1986).
R. V., Khachatryan, Dynamically stable optimality principle in multicriteria multistep game. Dokl. Akad. Nauk. Arm., SSR., 86 1 (1988), 23–26. (in Russian).
S. Y., Wang, An existence theorem of a Pareto equilibrium, Appl. Math. Lett., 4, 3 (1991), 61–63.
K. C., Border, Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, Cambridge (1985).
J. X., Zhou and G., Chen, Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities, J. Math. Anal. Appl., 132 (1988), 213–225.
G., Tian, Generalizations of the FKKM theorem and the Fan minimax inequality with applications to maximal elements, price equilibrium and complementarity. J. Math. Anal. Appl., 170 (1992), 457–471.
X. P., Ding, New H-KKM theorems and their applications to geometric property, coincidence theorems, minimax inequality and maximal elements, Indian J. Pure and Appl. Math., 26, 1 (1995), 1–19.
X. P., Ding, Best approximation and coincidence theorems, J. Sichuan Normal University, 18, 2 (1995), 21–29.
Fan, Ky, A miximax inequality and applications, Inequalities III, Ed. by O., Shisha Acad. Press, New York (1972), 103–113.
G., Allen, Variational inequalities, complementarity problems and duality theorems, J. Math. Anal. Appl., 58 (1977), 1–10.
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Xieping, D. Pareto equilibria of multicriteria games without compactness, continuity and concavity. Appl Math Mech 17, 847–854 (1996). https://doi.org/10.1007/BF00127184
Issue Date:
DOI: https://doi.org/10.1007/BF00127184