Open AccessModeling infinitely many agents
Author(s) -
He Wei,
Sun Xiang,
Sun Yeneng
Publication year - 2017
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te1647
Subject(s) - equivalence (formal languages) , lebesgue measure , unit interval , mathematical economics , property (philosophy) , measure (data warehouse) , space (punctuation) , game theory , mathematics , nowhere dense set , computer science , lebesgue integration , pure mathematics , discrete mathematics , philosophy , epistemology , database , operating system , set (abstract data type) , programming language
This paper offers a resolution to an extensively studied question in theoretical economics: which measure spaces are suitable for modeling many economic agents? We propose the condition of “nowhere equivalence” to characterize those measure spaces that can be effectively used to model the space of many agents. In particular, this condition is shown to be more general than various approaches that have been proposed to handle the shortcoming of the Lebesgue unit interval as an agent space. We illustrate the minimality of the nowhere equivalence condition by showing its necessity in deriving the determinateness property, the existence of equilibria, and the closed graph property for equilibrium correspondences in general equilibrium theory and game theory.