Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/the-study-of-minimax-inequalities-abstract-economics-and-applications-u7nPk0xDcy
References (57)
-
W. Kim, K. Tan (1992)
A variational inequality in non-compact sets and its applicationsBulletin of the Australian Mathematical Society, 46
-
K. Arrow, G. Debreu (1954)
EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMYEconometrica, 22
-
S. Y. Chang (1990)
On the Nash equilibriumSoochow J. Math., 16
-
J. Yu (1992)
On Nash equilibria inN-person games over reflexive Banach spacesJournal of Optimization Theory and Applications, 73
-
X. Ding, K. Tan (1992)
A minimax inequality with applications to existence of equilibrium point and fixed point theoremsColloquium Mathematicum, 63
-
X. Z. Yuan, E. Tarafdar (1996)
Enayet non-compact Pareto equilibria for multiobjective gamesJ. Math. Anal. Appl., 204
-
B. Ricceri (1985)
Un théorme d'existence pour les inéquationsC.R. Acad. Sci. Paris Ser. I Math., 301
-
G. Isac (1992)
Complementarity Problems -
M. Khan, Nikolaos Papageorgiou (1987)
On Cournot-Nash equilibria in generalized qualitative games with an atomless measure space of agents, 100
-
J. P. Aubin (1982)
Mathematical Methods of Game and Economics Theory -
D. Gale, A. Mas-Colell (1975)
An equilibrium existence theorem for a general model without ordered preferencesJournal of Mathematical Economics, 2
-
E. Michael (1956)
Continuous Selections. IAnnals of Mathematics, 63
-
T. Bewley (1972)
Existence of equilibria in economies with infinitely many commoditiesJournal of Economic Theory, 4
-
M. A. Khan, R. Vohra (1984)
Equilibrium in abstract economics without preferences and with a measure of agentsJ. Math. Econom., 13
-
C. Tulcea (1986)
On the Equilibriums of Generalized Games -
Wayne Shafer, H. Sonnenschein (1975)
Equilibrium in abstract economies without ordered preferencesJournal of Mathematical Economics, 2
-
X. Ding, W. Kim, K. Tan (1992)
Equilibria of non-compact generalized games with l∗-majorized preference correspondencesJournal of Mathematical Analysis and Applications, 164
-
N. Yannelis (1987)
Equilibria in noncooperative models of competitionJournal of Economic Theory, 41
-
U. TarafdarEnayet, G. Mehta (1987)
A generalized version of the Gale-Nikaido-Debréu theorem, 028
-
Guoqiang Tian (1992)
On the existence of equilibria in generalized gamesInternational Journal of Game Theory, 20
-
U. Mosco (1976)
Lecture Notes in Math. -
Kim Border (1985)
Fixed point theorems with applications to economics and game theory: References -
Atsushi Kajii (1988)
Note on equilibria without ordered preferences in topological vector spacesEconomics Letters, 27
-
T. Kim, K. Prikry, N. Yannelis (1989)
Equilibria in abstract economies with a measure space of agents and with an infinite dimensional strategy spaceJournal of Approximation Theory, 56
-
K. Tan, J. Yu (1994)
New minimax inequality with applications to existence theorems of equilibrium pointsJournal of Optimization Theory and Applications, 82
-
H. Kneser (1952)
Sur un théorème fondamental de la théorie des jeuxC.R. Acad. Sci. Paris, 234
-
Xian-Zhi Yuan, E. Tarafdar (1996)
Non-compact Pareto Equilibria for Multiobjective GamesJournal of Mathematical Analysis and Applications, 204
-
K. Fan (1952)
Fixed points and minimax theorems in locally convex topological linear spacesProc. Nat. Acad. Sci. USA, 38
-
I. Glicksberg (1952)
A FURTHER GENERALIZATION OF THE KAKUTANI FIXED POINT THEOREM, WITH APPLICATION TO NASH EQUILIBRIUM POINTS, 3
-
Sabine Toussaint (1984)
On the existence of equilibria in economies with infinitely many commodities and without ordered preferencesJournal of Economic Theory, 33
-
M. Florenzano (1983)
On the existence of equilibria in economies with an infinite dimensional commodity spaceJournal of Mathematical Economics, 12
-
W. Shafer (1976)
Equilibrium in economics without ordered preferences or free disposalJ. Math. Econom., 3
-
W. Kim (1988)
Remark on a generalized quasivariational inequality, 103
-
M.Ali Khan, R. Vohra (1984)
Equilibrium in abstract economies without ordered preferences and with a measure space of agentsJournal of Mathematical Economics, 13
-
T. Kim, M. Richter (1986)
Nontransitive-nontotal consumer theoryJournal of Economic Theory, 38
-
K. Tan, J. Yu, X. Yuan (1996)
Existence theorems for saddle points of vector-valued mapsJournal of Optimization Theory and Applications, 89
-
D. Gale, A. Mas-Colell (1975)
An equilibrium existence for a general model without ordered preferencesJ. Math. Econom., 2
-
G. Yuan (1998)
The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities -
Anders Borglin, H. Keiding (1976)
Existence of equilibrium actions and of equilibrium: A note on the ‘new’ existence theoremsJournal of Mathematical Economics, 3
-
T. Bergstrom, R. Parks, T. Rader (1976)
Preferences Which Have Open Graphs, 3
-
D. Gale, A. Mas-Colell (1977)
On the Role of Complete, Transitive Preferences in Equilibrium Theory -
N. Yannelis, N. Prabhakar (1983)
Existence of Maximal Elements and Equilibria in Linear Topological SpacesJournal of Mathematical Economics, 12
-
K. Tan, Xian-Zhi Yuan (1994)
Approximation method and equilibria of abstract economies, 122
-
J. Aubin, I. Ekeland (1984)
Applied Nonlinear Analysis -
T. Kim, K. Prikry, N. C. Yannelis (1989)
Equilibrium in abstract economics with a measure space and with an infinite dimensional strategy spaceJ. Approx. Theory, 56
-
S. D. Flam (1979)
Abstract economy and gamesSoochow J. Math., 5
-
K. Fan (1984)
Some properties of convex sets related to fixed point theoremsMathematische Annalen, 266
-
E. Klein, A. Thompson (1984)
Theory of correspondences : including applications to mathematical economics -
Xian-Zhi Yuan, E. Tarafdar (1996)
Existence of equilibria of generalized games without compactness and paracompactnessNonlinear Analysis-theory Methods & Applications, 26
-
Mau-Hsiang Shih, K. Tan (1985)
Generalized quasi-variational inequalities in locally convex topological vector spacesJournal of Mathematical Analysis and Applications, 108
-
D. Gale, A. Mas-Colell (1978)
Equilibrium and Disequilibrium in Economics Theory -
Gérard Debreu (1952)
A Social Equilibrium Existence Theorem*Proceedings of the National Academy of Sciences, 38
-
C. Tulcea (1988)
On the Approximation of Upper Semi-Continuous Correspondences and the Equilibriums of Generalized GamesJournal of Mathematical Analysis and Applications, 136
-
C. Aliprantis, Donald Brown (1983)
Equilibria in markets with a Riesz space of commoditiesJournal of Mathematical Economics, 11
-
H. Keiding (1984)
Lecture Notes in Econom. and Math. Systems -
Jianxin Zhou, Goong Chen (1988)
Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalitiesJournal of Mathematical Analysis and Applications, 132
-
Sze-Tsen Hu (1958)
Introduction to General Topology
- Publisher
- Springer Journals
- Copyright
- Copyright © 1998 by Kluwer Academic Publishers
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1023/A:1006095413166
- Publisher site
- See Article on Publisher Site
Abstract
In this survey, a new minimax inequality and one equivalent geometricform are proved. Next, a theorem concerning the existence of maximalelements for an LC-majorized correspondence is obtained.By the maximal element theorem, existence theorems of equilibrium point fora noncompact one-person game and for a noncompact qualitative game withLC-majorized correspondences are given. Using the lastresult and employing 'approximation approach', we prove theexistence of equilibria for abstract economies in which the constraintcorrespondence is lower (upper) semicontinuous instead of having lower(upper) open sections or open graphs in infinite-dimensional topologicalspaces. Then, as the applications, the existence theorems of solutions forthe quasi-variational inequalities and generalized quasi-variationalinequalities for noncompact cases are also proven. Finally, with theapplications of quasi-variational inequalities, the existence theorems ofNash equilibrium of constrained games with noncompact are given. Our resultsinclude many results in the literature as special cases.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Sep 18, 2004