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Existence Theorems for Maximal Elements in H-Spaces with Applications on the Minimax Inequalities and Equilibrium of Games
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X. Wu
Published/Copyright:
June 7, 2010
Abstract
In this paper, we give two new existence theorems for maximal elements in H-spaces. As their applications, we obtain a extended version of Fan–Yen minimax inequality and some new existence theorems of an equilibrium for a qualitative game and an abstract economy. Our main results not only generalize the corresponding results of [Fan, A minimax theorems and applications. Inequalities III, Academic Press, 1972, Tan and Yuan, J. Math. Econom. 23: 243–251, 1994, Yannelis and Prabhakar, J. Math. Econom. 12: 223–245, 1983, Yen, Pacific J. Math. 97: 477–481, 1981] to H-spaces, but also the open question raised by Yannelis and Prabhakar [J. Math. Econom. 12: 223–245, 1983] is answered in affirmative.
Key words and phrases.: H-space; -correspondence; Lθ-majorized correspondence; qualitative game; abstract economy
Received: 1998-07-21
Revised: 2000-01-18
Published Online: 2010-06-07
Published in Print: 2000-December
© Heldermann Verlag
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- Existence Theorems for Maximal Elements in H-Spaces with Applications on the Minimax Inequalities and Equilibrium of Games
- On Continuity of Measurable Cocycles
Keywords for this article
H-space;
-correspondence;
Lθ-majorized correspondence;
qualitative game;
abstract economy
Articles in the same Issue
- Category Analogue of Sup-Measurability Problem
- Lipschitzian Superposition Operators Between Spaces of Functions of Bounded Generalized Variation with Weight
- The Existence of Moments of Solutions to Transport Equations with Inelastic Scattering and their Application in the Asymptotic Analysis
- Graph Convergence of Set-Valued Maps and its Relationship to Other Convergences
- Local Existence of Solutions of a Free Boundary Problem for Equations of Compressible Viscous Heat-Conducting Capillary Fluids
- Quotients of Quasi-Continuous Functions
- Integrals of Legendre Polynomials and Solution of Some Partial Differential Equations
- Existence Theorems for Maximal Elements in H-Spaces with Applications on the Minimax Inequalities and Equilibrium of Games
- On Continuity of Measurable Cocycles
