Economies with a measure space of agents and a separable commodity space
نویسنده
چکیده
We prove the existence of an equilibrium in an economy with a measure space of agents and a separable Banach commodity space whose positive cone admits an interior point. We follow the truncation argument given at the end of Yannelis [Yannelis, N.C., 1987. Equilibria in noncooperative models of competition, J. Econ. Theory 41, 96–111] and the abstract economy approach as in Shafer [Shafer, W., 1976. Equilibrium in economies without ordered preferences or free disposal, J. Math. Econ. 3, 135–137] and Khan and Vohra [Khan, M.A., Vohra, R., 1984. Equilibrium in abstract economies without ordered preferences and with a measure space of agents, J. Math. Econ. 13, 133–142], which allows preferences to be interdependent. Our result may be viewed as an extension of the result in Kahn and Yannelis [Khan, M.A., Yannelis, N.C., 1991. Equilibria in markets with a continuum of agents and commodities. In: Khan, M.A., Yannelis, N.C. (Eds.), Equilibrium Theory in Infinite Dimensional Spaces, Springer-Verlag, Tokyo, pp. 233–248] employing production and allowing preferences to be interdependent. We utilize Mazur’s lemma at the crucial point in the truncation argument. We assume that the preference correspondence is representable by an interdependent utility function. The method in the present paper does not rely on the usual weak openness assumption on the lower sections of the preference correspondence. 2000 Elsevier Science B.V. All rights reserved.
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عنوان ژورنال:
- Mathematical Social Sciences
دوره 40 شماره
صفحات -
تاریخ انتشار 2000