Equilibria in abstract economies with a continuum of agents with discontinuous and non-ordered preferences

Anuj Bhowmik; Nicholas C. Yannelis

doi:10.1016/j.jmateco.2024.103049

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Equilibria in abstract economies with a continuum of agents with discontinuous and non-ordered preferences

Journal article

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Equilibria in abstract economies with a continuum of agents with discontinuous and non-ordered preferences

Anuj Bhowmik and Nicholas C. Yannelis

Journal of mathematical economics, Vol.115, 103049

12/2024

DOI: 10.1016/j.jmateco.2024.103049

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Abstract

This paper focus on the problem of the existence of an equilibrium in abstract economies and exchange economies. Spanning over the literature we have managed to extend and generalize some previous results. In particular, we generalize the main theorem of Yannelis (1987) on the existence of an equilibrium in an abstract economy with a continuum of agents, by allowing for discontinuous preferences. As a corollary of this result, we extend the finite agent Cournot–Nash equilibrium existence theorems with discontinuous preferences (e.g., Reny, 1999; Bareli and Meneghel, 2013; He and Yannelis, 2016; among others), to a continuum of agents. We also obtain an existence theorem for an abstract economy which allows for a convexifying effect on aggregation and nonconvex strategy and constraint sets. Furthermore, our new main theorem is used to prove the existence of a Walrasian equilibrium with a continuum of agents with discontinuous, non-ordered, interdependent and price-dependent preferences and thus extending the results of Aumman (1966) and Schmeidler (1969).

Continuous inclusion property

Abstract economy

Nash Equilibria

Existence of Walrasian equilibria

Details

Title: Subtitle: Equilibria in abstract economies with a continuum of agents with discontinuous and non-ordered preferences
Creators: Anuj Bhowmik - Indian Statistical Institute
Nicholas C. Yannelis - University of Iowa
Resource Type: Journal article
Publication Details: Journal of mathematical economics, Vol.115, 103049
Publisher: ELSEVIER SCIENCE SA; LAUSANNE
DOI: 10.1016/j.jmateco.2024.103049
ISSN: 0304-4068
eISSN: 1873-1538
Grant note: Science and Engineering Research Board (SERB): SERB/CRG/2023/009012
Anuj Bhowmik acknowledges financial support from the Science and Engineering Research Board (SERB Grant No. SERB/CRG/2023/009012) of India.
Language: English
Date published: 12/2024
Academic Unit: Economics
Record Identifier: 9984701245302771

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