Nash equilibrium and minimax theorem with \(\mathcal C\)-concavity
type: Item
instance of: scholarly article
title: Nash equilibrium and minimax theorem with \(\mathcal C\)-concavity
zbMATH Open document ID: 1108.91010
author: Won Kyu Kim
author: Kyoung Hee Lee
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-02-12T00:00:00Z
review text: The paper under review offers a new generalization of the Nash equilibrium theorem, which is well known in the non-cooperative game theory. Here, the generalization consists in the substitution of the linear structure of pay-offs by a modification of the concavity condition. Namely, the concept of the C-concavity generalizing both, the usual convexity and so called CF-convexity which combines continuity with a special form of concavity condition. The main result includes the proof of a new, generalized, theorem of a Nash equilibrium for non-compact generalized games. The result is applied to the proof of a new minimax theorem and of a minimax inequality.
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 90C47
Mathematics Subject Classification ID: 90B50
zbMATH DE Number: 5124026
zbMATH Keywords: Non-cooperative game
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: Quasiconvexity
zbMATH Keywords: C-concavity
zbMATH Keywords: Non-compact games
reviewed by: Milan Mareš
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.06.038
OpenAlex ID: W2023054479
cites work: Mathematical methods of game and economic theory
cites work: A Social Equilibrium Existence Theorem*
cites work: MARKET EQUILIBRIUM
cites work: Q3941926
cites work: Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces
cites work: Minimax Theorems
cites work: Q4057217
cites work: Q4296822
cites work: Q4166473
cites work: Fixed points of compact multifunctions
cites work: Q4010093
cites work: Q3774429
cites work: Q3774430
cites work: A note on Ky Fan's minimax theorem
cites work: Existence of Nash equilibria with \(\mathcal C\)-convexity
cites work: The existence of Nash equilibrium in \(n\)-person games with \(\mathcal C\)-concavity.
cites work: Efficiency and generalized concavity
cites work: Non-cooperative games
cites work: Note on noncooperative convex games
cites work: Existence of Nash Equilibrium in n Person Games without Quasi-Concavity
DOI: 10.1016/J.JMAA.2006.06.038
Recommended article: Existence of Nash equilibria with \(\mathcal C\)-convexity
Recommended article: Q4263514
Recommended article: The existence of Nash equilibrium in \(n\)-person games with \(\mathcal C\)-concavity.
Recommended article: Q3363113
Recommended article: Q3677543
Recommended article: Q4581773
Recommended article: Alternating minima and maxima, Nash equilibria and bounded arithmetic
Recommended article: Q4296822
Recommended article: The maximum theorem and the existence of Nash equilibrium of (generalized) games without lower semicontinuities
Recommended article: Generalizations of the Nash equilibrium theorem on generalized convex spaces
description: scientific article; zbMATH DE number 5124026