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
Combination Exchange Mechanisms for Efficient Bandwidth Allocation
Rahul Jain,Pravin Varaiya +1 more
TL;DR: It is shown that achieving economic efficiency through a market mechanism depends on network topology, and that in finite networks a competitive equilibrium may not exist, but a competitiveilibrium does exist in an idealized continuum model, in which all agents are infinitesimal compared with the size of the network.
9
•Dissertation
Game Theoretic Approaches to Spectrum Sharing in Decentralized Self-Configuring Networks
Samir M. Perlaza
- 08 Jul 2011
TL;DR: An alternative notion of equilibrium is formalized, namely satisfaction equilibrium (SE), which properly models the problem of QoS in DCSNs and allows radio devices to achieve NE in a fully decentralized fashion based only on the periodical observation of their individual performance.
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•Journal Article
Exploitation and Profits: A General Axiomatic Approach in Convex Economies with Heterogeneous Agents
TL;DR: In this paper, an axiomatic analysis of the notion of exploitation as the unequal exchange of labour, focusing on the relation between exploitation and proflts, is provided, and a characterisation of the class of deflnitions that preserve the Fundamental Marxian Theorem (FMT) in this general context is derived.
Coding for Wireless Broadcast and Network Secrecy
Tao Cui
- 01 Jan 2010
TL;DR: A cross-layer framework with wireless broadcast is developed, which integrates rate control, network coding and scheduling in transport, network and link layers, and it is shown that the link scheduling problem is the maximum weighted hypergraph matching problem, which is NP-complete.
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Affine equations as dynamic variables to obtain economic equilibria
Mitri Kitti
- 10 Feb 2006
TL;DR: In this article, the degree of doctor of technology, Helsinki University of Technology, Espoo, Finland, 10th of February, 2006, was given for the degree degree of Doctor of Technology.
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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