From Arrow–Debreu condition to star shape preferences. (1st November 2020)

• Record Type: Journal Article
• Authors: Braga de Freitas, Sinval; Orrillo, Jaime; Sosa, Wilfredo
• Is Part Of: Optimization. Volume 69:Number 11(2020)
• Page Start: 2405
• Page End: 2419
• Publication Date: 2020-11-01
• Subjects: Star shape sets -- generalized convexity -- preferences; 46N10 -- 47N10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1576664
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this work, we introduce the star shape preferences in the context of Economics Theory, based in the notion of star shape sets, introduced by Valentin in 1964. We develop our study from a condition introduced by Arrow and Debreu in their pioneer general equilibrium model of 1954. We prove that the closure of the strict preferred sets of a function satisfying this condition are star shaped. Moreover, when it has either convex effective domain or no maximizers, we show that the closure of its preferred and strict preferred sets are convex. Furthermore, we prove that this family of functions preserve some properties of concave functions and contains the whole family of pseudo-concave and semi-strictly quasi-concave functions that appear in the literature. Also, we prove that this family of functions induce star shape preferences.