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

Carlos Hervés-Beloso and Monica Patriche ()
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Monica Patriche: University of Bucharest

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 3, 719-736

Abstract: 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; 47H10; 91A47; 91A80 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-014-0548-0

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