Abstract
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.
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Armstrong, T.E. (1985). Remarks Related to Finitely Additive Exchange Economies. In: Aliprantis, C.D., Burkinshaw, O., Rothman, N.J. (eds) Advances in Equilibrium Theory. Lecture Notes in Economics and Mathematical Systems, vol 244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51602-3_10
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