Minimaximin results with applications to economic equilibrium
type: Item
instance of: scholarly article
title: Minimaximin results with applications to economic equilibrium
zbMATH Open document ID: 0563.90017
DOI: 10.1016/0304-4068(84)90035-1
published in: Journal of Mathematical Economics
publication date: 1984-01-01T00:00:00Z
review text: We suppose that \(f: P\times C\to R\) and \(E: P\to 2^ C\) are given. This paper gives conditions under which we can assert that there exists \(q\in P\) such that, for all \(p\in P\), there exists \(z\in E_ q\) such that f(p,z)\(\leq 0\). This problem has its origin in the theory of Walrasian equilibrium (in which P is a set of price levels, C is a set of commodity bundles, f(p,c) is the price of commodity bundle c at price level p and \(E_ p\) is the excess demand at price level p). Our results represent a considerable generalization of recent results of \textit{C. D. Aliprantis} and \textit{D. J. Brown} [ibid. 11, 189-207 (1983; Zbl 0502.90006)] in that they apply to concave-convex functions and excess demand correspondences rather than bilinear functions and excess demand functions. We do not assume that P is compact, but assume instead that f and E satisfy a certain boundary condition. We consider separately the cases when the sets \(E_ p\) are compact and the case when the sets \(E_ p\) are not assumed to be compact.
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 3898555
zbMATH Keywords: minimaximin results
zbMATH Keywords: existence of a free disposal equilibrium
zbMATH Keywords: infinite dimensional models of the economy
zbMATH Keywords: minimax theorems
zbMATH Keywords: fixed-point theorems
zbMATH Keywords: Walrasian equilibrium
zbMATH Keywords: boundary condition
author: Stephen Simons
MaRDI profile type: Publication
full work available at URL: 0304-4068(84)90035-1
OpenAlex ID: W1965553800
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description: scientific article; zbMATH DE number 3898555