zbMATH — the first resource for mathematics

Nash-type equilibrium theorems and competitive Nash-type equilibrium theorems. (English) Zbl 1103.91308
Summary: We consider two types of equilibrium problems. We study the constrained Nash-type equilibrium problems with multivalued payoff functions. We also study the competitive Nash-type equilibrium problems with multivalued payoff functions. In these two equilibrium problems, we want to find a strategy combination such that each player wishes to find a minimal loss from his multivalued payoff function. We use a fixed-point theorem of Park to prove the existence results of these two types of equilibrium problems.

91A10 Noncooperative games
91A44 Games involving topology, set theory, or logic
Full Text: DOI
[1] Ding, X.P., Existence of Pareto equilibria for constrained multiobjective games in H-space, Computers math. applic., 39, 9/10, 125-134, (2000) · Zbl 0960.91007
[2] Wang, S.Y., Existence of a Pareto equilibrium, J. optim. theory and appl., 79, 373-384, (1993) · Zbl 0797.90124
[3] Wang, S.Y., An existence theorem of a Pareto equilibrium, Appl. math. lett., 4, 3, 61-63, (1991) · Zbl 0744.90112
[4] Yu, J.; Yuan, G.X.-z., The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods, Computers math. applic., 35, 9, 17-24, (1998) · Zbl 1005.91008
[5] Nash, J., Noncooperative games, Ann. math., 54, 286-295, (1951) · Zbl 0045.08202
[6] Debreu, G., A social equilibrium theorem, (), 386-393
[7] Park, S., (), 248-277
[8] Luc, D.T.; Vargas, C., A saddle point theorem for set-valued maps, Nonlinear anal., theory, methods & applications, 18, 1-7, (1992)
[9] Lin, L.J.; Yu, Z.T., On generalized vector quasi-equilibrium problems for multimaps, J. computational and applied math., 129, 171-183, (2001)
[10] Aubin, J.P.; Frankowska, H., Set-valued analysis, (1990), Springer-Verlag Birkhauser, Boston, MA
[11] Lassonde, M., On the use of KKM multifunctions in fixed point theory and related topics, J. math. anal. appl., 97, 151-201, (1983) · Zbl 0527.47037
[12] Horvath, C.D., Extensions and selection theorems in topological vector space with a generalized convexity structure, Ann. fac. sci. Toulouse, 2, 253-269, (1993) · Zbl 0799.54013
[13] Lee, B.S.; Lee, G.M.; Chang, S.S., Generalized vector variational inequalities for multifunctions, (), 193-202 · Zbl 1012.47050
[14] Luc, D.T., ()
[15] Massey, W.S., Singular homology theory, (1980), Springer Verlag New York · Zbl 0377.55005
[16] Fan, K., Fixed point and minimax theorems in locally convex topological linear spaces, Pro. nat. acad. sci. U.S.A., 38, 121-126, (1952) · Zbl 0047.35103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.