A Fixed-Point Theorem and Equilibria of Abstract Economies with Weakly Upper Semicontinuous Set-Valued Maps
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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.
KeywordsFixed-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
We are grateful to the editor and two anonymous reviewers for their valuable suggestions that have improved the quality of the paper. The first author thanks the support by Research Grants ECO2012-38860-C02-02 (Ministerio de Economia y Competitividad), RGEA and 10PXIB300141PR (Xunta de Galicia and FEDER).
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