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EXISTENCE AND UNIQUENESS OF EQUILIBRIUM FOR A SPATIAL MODEL OF SOCIAL INTERACTIONS*
Author(s) -
Blanchet Adrien,
Mossay Pascal,
Santambrogio Filippo
Publication year - 2016
Publication title -
international economic review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.658
H-Index - 86
eISSN - 1468-2354
pISSN - 0020-6598
DOI - 10.1111/iere.12147
Subject(s) - uniqueness , convexity , class (philosophy) , space (punctuation) , displacement (psychology) , mathematical economics , mathematics , mathematical optimization , economics , computer science , mathematical analysis , psychology , artificial intelligence , financial economics , psychotherapist , operating system
We extend Beckmann's spatial model of social interactions to the case of a two‐dimensional spatial economy with a large class of utility functions, accessing costs, and space‐dependent amenities. We show that spatial equilibria derive from a potential functional. By proving the existence of a minimizer of the functional, we obtain that of spatial equilibrium. Under mild conditions on the primitives of the economy, the functional is shown to satisfy displacement convexity. Moreover, the strict displacement convexity of the functional ensures the uniqueness of equilibrium. Also, the spatial symmetry of equilibrium is derived from that of the primitives of the economy.