Journal of Optimization Theory and Applications

, Volume 163, Issue 3, pp 719–736

A Fixed-Point Theorem and Equilibria of Abstract Economies with Weakly Upper Semicontinuous Set-Valued Maps

Article

Abstract

The main purpose of this paper is to introduce the notion of weakly upper semicontinuous set-valued maps and to establish a new fixed-point theorem. The set-valued maps with an approximating upper semicontinuous selection property are also defined. Next, we use our fixed-point result to obtain equilibrium existence in abstract economies with two constraints, which provide a natural scenario for potential applications of our approach to general equilibrium theory. In this regard, we set models of economies with asymmetric informed agents, who are able to improve their initial information through market signals. These economies offer examples in which the informational feasibility requirement represents an additional constraint.

Keywords

Fixed-point theorem W-upper semicontinuous set-valued maps Set-valued maps with e-USS property Abstract economy Equilibrium 

Mathematics Subject Classification (2010)

47H10 91A47 91A80 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.RGEA, Facultad de EconómicasUniversidad de VigoVigoSpain
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania

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