Remarks Related to Finitely Additive Exchange Economies

Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 244)


Inspired mainly by the desire to work with perfectly competitive exchange economies with only countably many agents Brown, Pallaschke, Klein, Weiss and Armstrong-Richter have examined economies given by non-atomic finitely additive (rather than countably additive) measures. In Section 2 a fairly standard measure theoretic model of perfect competition is presented. In Section 3 it is seen based on Skala in part, that assumptions of fewer than \( C = {2^{\aleph {}_0}}\) traders forces one to drop countable additivity (subject to one’s axioms of set theory). In Section 4 another reason to drop the assumption of countable additivity is examined. This is the consideration of the limit economies of a non-tight perfectly competitive sequence of finite economies. In Section 7 a rather “constructive” model of coalition formation is given based on work of Klein leading naturally only to algebras of coalitions rather than σ-algebras. In this context the assumption of countable additivity is often unnatural or unverifiable.


Exchange Economy Polish Space Coalition Formation Measurable Cardinal Core Allocation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of Maryland-Baltimore CountyBaltimoreUSA

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