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
Common Fixed Points of Expansive Mappings in Generalized Metric Spaces
TL;DR: In this paper, the authors established a common fixed point theorem for expansive mappings by using the concept of weakcompatibility in the setting of G-metric spaces, which generalizes the result of Ahmed and Telci [2] from 2-mappings to G-mapping by removing the condition of sequential continuity of mappings.
4
Characterization and computation of control invariant sets for linear impulsive control systems
TL;DR: In this article , a method for characterizing and computing approximations to the maximal control invariant sets for linear impulsive control systems is developed, which can be explicitly used to formulate a set-based model predictive controller.
4
The LSB Theorem Implies the KKM Lemma
Gwen Spencer,Francis Edward Su +1 more
TL;DR: The LSB Theorem Implies the KKM Lemma as mentioned in this paper, which is the LSB theorem that implies the k-means-theorem of the KLM. The American Mathematical Monthly: Vol. 114, No. 2, pp. 156-159
Failing to forecast rare events
Philip Bond,James Dow +1 more
TL;DR: The authors show that lower skill traders prefer to bet on rare events, while higher skill traders bet on and against frequent events, leading to higher bid-ask spreads in common event assets, and reducing financial markets' ability to predict rare events.
4
Parameter estimation by fixed point of function of information processing intensity
TL;DR: In this paper, a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity was proposed, and it turns out that this function has a maximum at its fixed point.
4
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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