Abstract
In this paper we consider the Nash equilibrium problem for infinite player games with vector payoffs in a topological vector space setting. By employing new concepts of relative (pseudo)monotonicity, we establish several existence results of solutions for usual and normalized vector equilibria. The results strengthen existence results for vector equilibrium problems, which were based on classical pseudomonotonicity concepts. They also extend previous results for vector variational inequalities and finite player games under relative (pseudo)monotonicity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Allevi A. Gnudi I.V. Konnov (2001) ArticleTitleGeneralized vector variational inequalities over product sets Nonlinear Analysis 47 573–582 Occurrence Handle10.1016/S0362-546X(01)00202-4
E. Allevi A. Gnudi I.V. Konnov S. Schaible (2003) ArticleTitleNoncooperative games with vector payoff under relative pseudomonotonicity Journal of Optimization Theory and Applications 118 245–254 Occurrence Handle10.1023/A:1025491103925
D. Blackwell (1956) ArticleTitleAn analogue of the minimax theorem for vector payoffs Pacific Journal of Mathematics 6 1–8
M. Bianchi N. Hadjisavvas S. Schaible (1997) ArticleTitleVector equilibrium problems with generalized monotone bifunctions Journal of Optimization Theory and Applications 92 527–542 Occurrence Handle10.1023/A:1022603406244
K. Fan (1984) ArticleTitleSome properties of convex sets related to fixed-point theorems Mathematische Annalen 266 519–537 Occurrence Handle10.1007/BF01458545
F. Giannessi (2000) Vector Variational Inequslities and Vector Equilibria. Mathematical Theories Kluwer Academic Publishers Dordrecht The Netherlands
N. Hadjisavvas S. Schaible (1998) Quasimonotonicity and pseudomonotonicity in variational inequalities and equilibrium problems J.-P. Crouzeix J.E. Martinez-Legaz M. Volle (Eds) Generalized Convexity, Generalized Monotonicity Kluwer Academic Publishers Dordrecht, The Netherlands 257–275
I.V. Konnov (1995) ArticleTitleCombined relaxation methods for solving vector equilibrium problems Russ. Mathematics (Iz. VUZ) 39 IssueID12 51–59
I.V. Konnov (2001) ArticleTitleRelatively monotone variational inequalities over product sets Operations Research Letters 28 21–26 Occurrence Handle10.1016/S0167-6377(00)00063-8
I.V. Konnov S. Schaible (2000) ArticleTitleDuality for equilibrium problems under generalized monotonicity Journal of Optimization Theory and Applications 104 395–408 Occurrence Handle10.1023/A:1004665830923
A. Nagurney (1993) Network Economics: A Variational Inequality Approach Kluwer Academic Publishers Dordrecht, The Netherlands
H. Nikaido K. Isoda (1955) ArticleTitleNote on noncooperative convex games Pacific Journal of Mathematics 5 807–815
V.V. Podinovskii V.D. Nogin (1982) Pareto-optimal Solutions of Multicriteria Problems Nauka Moscow
J.B. Rosen (1965) ArticleTitleExistence and uniqueness of equilibrium points for concave n-person games Econometrica 33 520–534
J. Neumann Particlevon O. Morgenstern (1953) Game Theory and Economic Behavior Princeton University Press Princeton, N.J
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Allevi, E., Gnudi, A., Konnov, I.V. et al. Infinite Player Noncooperative Games with Vector Payoffs Under Relative Pseudomonotonicity. J Glob Optim 34, 79–96 (2006). https://doi.org/10.1007/s10898-005-4387-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10898-005-4387-2