Open AccessBook
Fixed Point Theorems with Applications to Economics and Game Theory
Kim C. Border
- 26 Apr 1985
633
TL;DR: This book gives the reader access to the mathematical techniques involved and goes on to apply fixed point theorems to proving the existence of equilibria for economics and for co-operative and noncooperative games.
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Abstract: Preface 1. Introduction: models and mathematics 2. Convexity 3. Simplexes 4. Sperner's lemma 5. The Knaster-Kuratowski-Mazurkiewicz lemma 6. Brouwer's fixed point theorem 7. Maximization of binary relations 8. Variational inequalities, price equilibrium, and complementarity 9. Some interconnections 10. What good is a completely labelled subsimplex? 11. Continuity of correspondences 12. The maximum theorem 13. Approximation of correspondence 14. Selection theorems for correspondences 15. Fixed point theorems for correspondences 16. Sets with convex sections and a minimax theorem 17. The Fan-Browder theorem 18. Equilibrium of excess demand correspondences 19. Nash equilibrium of games and abstract economies 20. Walrasian equilibrium of an economy 21. More interconnections 22. The Knaster-Kuratowski-Mazurkiewicz-Shapley lemma 23. Cooperative equilibria of games References Index.
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Citations
An Implication of the Existence of Competitive Equilibrium
Anjan Mukherji
- 17 Nov 2006
TL;DR: One of the most fundamental propositions in economic theory is that a competitive equilibrium exists as discussed by the authors, which is entirely non-intuitive about this proposition is the fact that the set of assumptions, which allows a wide variety of decision makers to do their own thing, is mutually consistent.
1
Pure exchange competitive equilibrium under uncertainty
Qiqiong Chen,Yuanguo Zhu +1 more
TL;DR: This paper investigates a version of pure exchange competitive equilibrium under uncertain circumstances that is applied in a pure exchange economy which consists of two agents and two goods and finds the competitive equilibrium of this economy with each agent’s preference being an uncertain variable.
1
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On the General Existence of Pure Strategy Political Competition Equilibrium in Multi-dimensional Party-Faction Models
TL;DR: In this article, the authors consider political competition games of two parties in multi-dimensional policy spaces, where the two parties have two factions, opportunists and militants, that intra-party bargain with each other.
Best proximity point theorems in partially ordered metric spaces
TL;DR: The notion of generalized Berinde type contraction non-self maps in partially ordered metric spaces was introduced in this article, and some best proximity point theorems for this class were established.
1
On logit dynamics in population games
L Cianfanelli,Giacomo Como +1 more
TL;DR: In this article , the authors studied the logit evolutionary dynamics in population games and proved that strict Nash equilibria are locally asymptotically stable under the dynamics in the low noise regime, while a globally exponentially stable fixed point exists in the high noise regime.
References
Existence of an equilibrium for a competitive economy
Kenneth J. Arrow,Gerard Debreu +1 more
TL;DR: In this article, a simplification of the structure of the proofs has been made possible through use of the concept of an abstract economy, a generalization of that of a game, and proofs of the existence of an equilibrium are given for an integrated model of production, exchange and consumption.
On some non-linear elliptic differential-functional equations
TL;DR: In this paper, the results to be obtained can be considered as generalizations of some theorems of Gilbarg [5] and Stampacchia [14] in the case F [ u ] ~ 0.
•Book
The Computation of Fixed Points and Applications
Michael J. Todd
- 01 May 1976
TL;DR: In this paper, Brouwer's Theorem and its extensions have been used to find completely labeled simplices. But the complexity of these simplices has not been studied.
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