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
Opinion propagation on social networks: a Mathematical Standpoint
Hugo Lavenant,Bertrand Maury +1 more
TL;DR: These lecture notes address mathematical issues related to the modeling of opinion propagation on networks of the social type with various standpoints and describe some extensions: stochastic interpretation, monitoring of a network, time continuous evolution problem, charismatic networks, links with discretized Partial Differential Equations, nonlinear models, inertial version and stability issues.
•Book
Political Preferences and the Aging of Populations: Political-Economy Explanations of Pension Reform
Oliver Pamp
- 16 Jan 2015
TL;DR: In this paper, a political-economy model was proposed for individual pension reform preferences and reform in a cross-national survey of the United States population, based on a model of the economy.
Firms as Clubs in Walrasian Markets with Private Information: Technical Appendix
TL;DR: In this article, the authors proved the welfare theorem and the existence of a competitive equilibrium for the club economy with private information in Prescott and Townsend (2005) and showed that the same theorem holds also for the private information game.
•Posted Content
On the Interplay between Self-Driving Cars and Public Transportation
Nicolas Lanzetti,Maximilian Schiffer,Michael Ostrovsky,Marco Pavone +3 more
- 03 Sep 2021
TL;DR: In this paper, a graph-theoretic network model for the transportation system is combined with a game theoretic market model in which mobility service providers are profit-maximizers, while customers select individually-optimal transportation options.
10
A dynamic game of coalition formation under ambiguity
Giuseppe De Marco,Maria Romaniello +1 more
- 01 Apr 2010
TL;DR: It is found that if the multiplicity of coherent beliefs problem is approached by considering “ambiguity loving” players then existence results for classical static equilibria can be obtained in this model.
10
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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