General theory of equilibrium in models with complementarities

Tarun Sabarwal

No 202307, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: We unify and generalize the equilibrium theory of foundational models of complementarities used widely in economics and other disciplines. Widely used results for existence of extremal equilibrium, nonempty complete lattice structure of the equilibrium set, and monotone comparative statics (MCS) of extremal equilibria are unified and generalized, subsuming the results for standard and neostandard models as special cases and allowing for new situations. Structure theorems due to Tarski (1955) and Zhou (1994) are generalized without using the strong set order or subcompleteness. Defining new set orders, we formulate new theories for structural comparisons of equilibrium sets, and prove new theorems for MCS of the infimum equilibrium set, the supremum equilibrium set, and the full equilibrium set. Order comparability of equilibrium sets provides a new theory of order approximation of equilibria as well. Our off-the-shelf theorems apply regardless of the manner in which individual choices are made as long as they satisfy our weak conditions, which are proved to hold in standard and neostandard models.

Keywords: Complementarities; Equilibrium; Fixed point; Strategic complements; Monotone comparative statics (search for similar items in EconPapers)
JEL-codes: C62 C72 D70 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2023-04, Revised 2023-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Journal Article: General theory of equilibrium in models with complementarities (2025)
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