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
Characterization of a topological obstruction to reach control by continuous state feedback
TL;DR: The results of this paper represent the culmination of efforts to characterize the topological obstruction and remove unnecessary restrictions on the dimension of the simplex, the number of inputs of the system, and the particular geometry of the subset of the state space where the obstruction arises.
6
•Posted Content
General Equilibrium with Endogenous Trading Constraints
Sebastián Cea-Echenique,Juan Pablo Torres-Martínez +1 more
- 01 Jan 2014
TL;DR: In this paper, a general equilibrium model where agents are subject to endogenous trading constraints, making the access to financial trade dependent on prices and consumption decisions is proposed. But the model is not compatible with the existence of endogenous financial segmentation and credit markets' exclusion.
6
General financial equilibrium with policy interventions: a variational inequality approach
TL;DR: A model of general financial equilibrium with policy interventions is introduced, which yields the optimal composition of assets and liabilities in each sector's portfolio, as well as the market prices for each instrument.
6
Cone concavity and multiple-payoff constrained n -person games
TL;DR: In this paper, the authors investigated special cases of abstract economies, i.e., n-person games with multiple payoff functions, and obtained sufficient and necessary conditions for such multiple payoff constrained n-player games.
6
Dynamic Information Regimes in Financial Markets
TL;DR: In this paper, a model of investor information choices and asset prices where the availability of information about fundamentals is time-varying is developed, which generates two regimes in equilibrium, one having high prices and low volatility, the other the opposite.
6
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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