An Approximation Method for Evolutions of Exchange Economies Making the Evolving Equilibrium Set Nice

Abstract

Static equilibrium theory still struggles with the annoying feature of indeterminateness of the equilibrium set. For evolutions of exchange economies, however, there is a certain general well-behavedness property of the evolving equilibrium set (Mas-Colell, Lehmann-Waffenschmidt). Unfortunately, this property is rather weak. Mas-Colell has shown by an abstract argumentation that in principle it must be possible to approximate evolutions so that a significantly stronger well-behavedness property obtains. Our present paper presents an explicit method which achieves the approximation. Based on the familiar polynomial approximation our method seems both natural and intuitive. Major efforts, however, were necessary to verify the well-behavedness of the evolving equilibrium set.

The authors are indebted to Prof. R. Selten, University of Bonn, who suggested the issue of polynomial approximation, and to Prof. C. T. C. Wall, University of Liverpool, who indicated the reference to Teissier’s article.