Computation of Fisher-Gale equilibrium by auction
type: Item
instance of: scholarly article
title: Computation of Fisher-Gale equilibrium by auction
zbMATH Open document ID: 1416.91139
author: Vladimir Shikhman
author: Yuri Nesterov
published in: Journal of the Operations Research Society of China
publication date: 2018-08-10T00:00:00Z
review text: The paper suggests an algorithm for computing an equilibrium in the Fisher model of a competitive market, which is an early development of the Walras equilibrium theory with two finite sets of agents that are thought independent and rational: consumers (buyers) having fixed quantities of money, and producers of goods (sellers). Each producer supplies fixed amounts of goods, and consumers spend all their money on obtaining bundles that maximize their individual utility functions. This conceptual normative model of artificial economy (in view of impossibility to know the numbers of elementary agents and to estimate their characteristics in real markets and economies) was later generalized by \textit{K. J. Arrow} and \textit{G. Debreu} [Econometrica 22, 265--290 (1954; Zbl 0055.38007)]. The latter is the cornerstone of contemporary neoclassical equilibrium theory till now in spite of strong deficiencies of this model which was revealed at the middle of 20-th century. These deficiencies are being discussed, particularly, in the papers by \textit{A. Kirman} [``Whom or what does the representative individual represent?'', J. Econ. Perspect. 6, No. 2, 117--136 (1992; \url{doi:10.1257/jep.6.2.117}); ``The economic crisis is a crisis for economic theory'', CESifo Econ. Stud. 56, No. 4, 498--535 (2010)], by \textit{V. Polterovich} [``Crisis of economics'', Ekonomicheskaya Nauka Sovremennoy Rossii, No. 1, 46--66 (1998)], and by \textit{V. K. Gorbunov} [Econ. Nauka Sovrem. Ross. 2013, No. 4, 19--36 (2013; Zbl 1310.91089); Dokl. Math. 98, No. 2, 537--539 (2018; Zbl 1419.91448); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 482, No. 3 (2018)]. However, the Fisher market model can be considered as a model of international trade with agents-states. Such a real object can be observed and its quantitative analysis will need computational methods. The authors construct their computational method in frame of the \textit{E. Eisenberg} and \textit{D. Gale}'s method [Ann. Math. Stat…
reviewed by: Vladimir Gorbunov
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91-08
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 6915968
zbMATH Keywords: general equilibrium
zbMATH Keywords: Fisher-Gale equilibrium
zbMATH Keywords: computation of equilibrium
zbMATH Keywords: convex optimization
zbMATH Keywords: tatonnement
zbMATH Keywords: consumers prices
zbMATH Keywords: auction
MaRDI profile type: Publication
full work available at URL: s40305-018-0195-5
OpenAlex ID: W1725699329
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DOI: 10.1007/S40305-018-0195-5
description: scientific article; zbMATH DE number 6915968