A fixed point theorem and equilibrium point of an abstract economy

Tarafdar, E.

doi:10.1016/0304-4068(91)90010-q

Cited by 66 publications

(49 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our results are stated for not-necessarily locally convex topological vector spaces and for abstract economies with arbitrary number of commodities and agents. Consequently, our new results extend a lot of known works due to von Neumann [71], Nash [41], Fan [11,12,13,14], Ma [37], Idzik [21,22], Yannelis and Prabhakar [73], Tarafdar [69], Kim and Tan [30], and others, with much simpler proofs. Recall that a nonempty topological space is acyclic if all of its reducedCech homology groups over rationals vanish.…”

Section: Introductionsupporting

confidence: 78%

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

Park

2000

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

Abstract. 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.

show abstract

Section: Introductionsupporting

confidence: 78%

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

Park

2000

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…Over the last twenty y ears, more general existence results appeared in the literature. To make a partial list of these results we mention Borglin and Keiding 1976], Yannelis and Prabhakar 1983], Toussaint 1983], Yannelis 1987], Tarafdar 1989], and Tan and Yuan 1994]. All of these results however, assume directly or indirectly the lower semi-continuity of the set valued map representing the constraints for each agent.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium in abstract economies without the lower semi-continuity of the constraint maps

Bagh

1998

Journal of Mathematical Economics

View full text Add to dashboard Cite

Abstract. We use graph convergence of set valued maps to show the existence of an equilibrium for an abstract economy without assuming the lower semi continuity of the constraint maps.Keywords: abstract economy, equilibrium, set convergence, set valued maps, L-majorized maps, Walrasian equilibrium. In this paper, we will use the concept of graphical convergence of set-valued maps to show that an equilibrium for an abstract economy exists without such an assumption. Eliminating the requirement o f t h e l o wer semi-continuity of the constraint map is not just technical improvement. It will actually make the setting of the abstract economy more realistic as we will demonstrate at the end of the paper. We s t a r t b y reviewing the mathematical and the economical concepts that we need. Then, we p r o ve s e v eral results regarding the existence of equilibria for abstract economies without assuming the lower semi-continuity o f t h e of the constraint map. Finally, w e discuss some of the economical implications of the new results.

show abstract

“…Let / be a countable or uncountable set of agents. We shall describe an abstract economy by F = (Qi,Fi,Gi,Pi) i€l where for each i e I, Qi(C Ei) is the choice (or strategy) set, Fi, Gi : fl Qi = Q -> % Qi are contraint correspondences and P t : Q -¥ 2 Qi is a preference correspondence (see [8,9] …”

Section: Is a Condensing Map With G(q) A Subset Of A Bounded Set In Ementioning

confidence: 99%

Fixed point theorems and equilibrium points in abstract economies

O’Regan

1998

Bull. Austral. Math. Soc.

View full text Add to dashboard Cite

show abstract

A fixed point theorem and equilibrium point of an abstract economy

Cited by 66 publications

References 16 publications

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

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

Equilibrium in abstract economies without the lower semi-continuity of the constraint maps

Fixed point theorems and equilibrium points in abstract economies

Contact Info

Product

Resources

About