Cores of dense exchange economies

Dense exchange economies cardinal characteristic is that each trader has infinitely many traders close to him or her in terms of initial allocations of goods and preference orderings. For such economies, a qualitative concept of “core” is formulated, and it is shown that a natural, qualitatively defined subset of the core coincides with the quantitative concept of “competitive equilibria.” The method of proof avoids the use of the Axiom of Choice. Dense exchange economies and other exchange economies are also discussed with respect to the appropriateness of the kinds of infinitistic assumptions used in their formulations and in the obtaining of characterizing theorems.