article Open AccessTop 10% cited
A further generalization of the Kakutani fixed theorem, with application to Nash equilibrium points
Proceedings of the American Mathematical Society · 1952 · Vol. 3(1) · pp. 170–174
Abstract
Introduction. Kakutani's fixed point theorem Kakutani showed that this implied the minimax theorem for finite games. The object of this note is to point out that Kakutani's theorem may be extended to convex linear topological spaces, and implies the minimax theorem for continuous games with continuous payoff as well as the existence of Nash equilibrium points.
Game Theory and Voting SystemsGame Theory and ApplicationsOptimization and Variational AnalysisGeneralizationMathematical economicsFixed-point theoremKakutani fixed-point theoremMathematicsNash equilibriumBrouwer fixed-point theoremPure mathematicsMathematical analysisSchauder fixed point theorem
Citations
831
FWCI
15.52
field-weighted impact
References
10
Percentile
97%
vs. same field & year
Citations per year
Cited by
Efficient power control via pricing in wireless data networks
IEEE Transactions on Communications · 2002 · 1,335 citations
Power control in two-tier femtocell networks
IEEE Transactions on Wireless Communications · 2009 · 754 citations
The Existence of Equilibrium in Discontinuous Economic Games, I: Theory
The Review of Economic Studies · 1986 · 1,045 citations
References
Equilibrium points in <i>n</i> -person games
Proceedings of the National Academy of Sciences · 1950 · 7,211 citations
Citation Network
How this paper connects to the literature. Drag to explore, click any node to open that paper.