A fixed point theorem and existence of equilibrium for abstract economies

1992 ◽  
Vol 45 (3) ◽  
pp. 385-394 ◽  
Author(s):  
Dong Il Rim ◽  
Won Kyu Kim
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Equilibrium Points ◽  
Utility Functions ◽  
Existence Of Equilibrium ◽  
Abstract Economies

In this paper, we shall prove a generalisation of Himmelberg's fixed point theorem and as applications, the existence of equilibrium points for abstract economies given by preference correspondences and utility functions have been established.

Brauer's Fixed Point Theorem

2021 ◽  
Vol 8 (1) ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Simple Proof ◽  
Exchange Model ◽  
Existence Of Equilibrium ◽  
Economic Applications ◽  
Brouwer’S Fixed Point Theorem ◽  
Brouwer's Fixed Point Theorem

The primary goal of the paper is to deliver a simple proof of equivalence between Brouwer’s fixed point theorem and the existence of equilibrium in a simple exchange model with monotonic consumers. To achieve this end, we discuss some equivalent formulations of Brouwer’s theorem and prove additional ones, that are ’approximating’ in character or seem to be better suited for economic applications than the standard results.

scholarly journals A Collectively Fixed Point Theorem in Abstract Convex Spaces and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Haishu Lu ◽  
Qingwen Hu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Theorems ◽  
Abstract Economies ◽  
Collectively Fixed Point ◽  
Convex Spaces

The main purpose of this paper is to establish a new collectively fixed point theorem in noncompact abstract convex spaces. As applications of this theorem, we obtain some new existence theorems of equilibria for generalized abstract economies in noncompact abstract convex spaces.

scholarly journals Duplex selections, equilibrium points, and viability tubes

2018 ◽  
Vol 27 (2) ◽  
pp. 19-33
Author(s):  
Zoltán Kánnai
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Equilibrium Points ◽  
Time Dependent ◽  
Equilibrium Form ◽  
Selection Theorem ◽  
Convex Case

Abstract Existence of viable trajectories to nonautonomous differential inclusions are proven for time-dependent viability tubes. In the convex case we prove a double-selection theorem and a new Scorza-Dragoni type lemma. Our result also provides a new and palpable proof for the equilibrium form of Kakutani’s fixed point theorem.

On Equilibrium for Abstract Economies in GFC-Spaces

2014 ◽  
Vol 587-589 ◽  
pp. 2279-2284
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Kkm Mapping ◽  
Equilibrium Existence ◽  
Abstract Economies ◽  
Element Theorem ◽  
Qualitative Games

In this paper, the GFC-KKM mapping is introduced and GFC-KKM theorems are established in GFC-spaces. As applications, a fixed point theorem and maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, equilibrium existence theorems for qualitative games and abstract economies are yielded in GFC-spaces.

A fuzzy fixed-point theorem and its applications to maximal elements and Nash equilibria in noncompact CAT(0) spaces

2022 ◽  
pp. 1-18
Author(s):  
Haishu Lu ◽  
Rong Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Equilibrium Points ◽  
Maximal Elements ◽  
Nash Equilibrium Points ◽  
Fuzzy Fixed Point ◽  
Qualitative Games

In this paper, based on the KKM method, we prove a new fuzzy fixed-point theorem in noncompact CAT(0) spaces. As applications of this fixed-point theorem, we obtain some existence theorems of fuzzy maximal element points. Finally, we utilize these fuzzy maximal element theorems to establish some new existence theorems of Nash equilibrium points for generalized fuzzy noncooperative games and fuzzy noncooperative qualitative games in noncompact CAT(0) spaces. The results obtained in this paper generalize and extend many known results in the existing literature.

scholarly journals Fixed points, intersection theorems, variational inequalities, and equilibrium theorems

2000 ◽  
Vol 24 (2) ◽  
pp. 73-93 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Convex Sets ◽  
Quasi Equilibrium ◽  
Topological Vector Spaces ◽  
Abstract Economies ◽  
General Economic Equilibrium ◽  
Locally Convex

From a fixed point theorem for compact acyclic maps defined on admissible convex sets in the sense of Klee, we first deduce collectively fixed point theorems, intersection theorems for sets with convex sections, and quasi-equilibrium theorems. These quasi-equilibrium theorems are applied to give simple and unified proofs of the known variational inequalities of the Hartman-Stampacchia-Browder type. Moreover, from our new fixed point theorem, we deduce new variational inequalities which can be used to obtain fixed point results for convex-valued maps. Finally, various general economic equilibrium theorems are deduced in the forms of the Nash type, the Tarafdar type, and the Yannelis-Prabhakar type. Our results are stated for not-necessarily locally convex topological vector spaces and for abstract economies with arbitrary number of commodities and agents. Our new results extend a lot of known works with much simpler proofs.

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