Equilibria Without the Survival Assumption: A Non-Standard Analysis Approach

A. Konovalov, V. Marakulin

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Abstract

It is well known that an equilibrium in the Arrow-Debreu model may fail to exist if a very restrictive condition called the survival assumption is not satisfied.We study two approaches that allow for the relaxation of this condition.Danilov and Sotskov (1980), and Florig (1998a) developed a concept of a generalized equilibrium based on a notion of hierarchic prices.Marakulin (1988, 1990) proposed a concept of an equilibrium with non-standard prices.In this paper, we establish the equivalence between non-standard and hierarchic equilibria.Furthermore, we show that the set of non-standard equilibria coincides with the fuzzy rejective core of an economy and is generically finite for any specified system of dividends.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages43
Volume2001-34
Publication statusPublished - 2001

Publication series

NameCentER Discussion Paper
Volume2001-34

Keywords

  • equilibrium theory

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    Konovalov, A., & Marakulin, V. (2001). Equilibria Without the Survival Assumption: A Non-Standard Analysis Approach. (CentER Discussion Paper; Vol. 2001-34). Microeconomics.