Abstract
We show that for an open dense set of markets with a continuum of traders the number of equilibrium allocations [which by the celebrated theorem of Aumann ( Econometrica. 1964, 32. 39–50) coincide with the core allocations for such markets are finite. This presents a limiting case result that complements similar asymptotic theorems for cores of large economies proved by Bewley ( Econometrica 1973, 41, 425–454) , and Dierker ( Journal of Mathematical Economics 1975, 2. 155–169) . If we require that the measure on the space of agents be one with a finite number of atoms of equal weight, our reasoning recovers the classical results obtained by Debreu ( Econometrica. 1970. 38, 387–392) for economies with a finite number of agents.
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