Continuous representation of preference
In this paper we study a utility representation for preferences, and we price its continuity, using a topology for preferences introduced by Chichilnisky (1977). Such utility representations were constructed under restrictive conditions first by Y. Kannai and S. Reiter (1974, 1975). Our results are related more closely to those of Mount and Reiter (1974 and 1975). Starting from restrictive conditions these works have attempted to enlarge the class of preferences that could be continuously represented. The class of preferences studied here is much larger than those considered earlier, and it therefore applies to a wider class of problems. Our preferences include ones which are not necessarily convex or monotone, and which may be locally satiated; furthermore, no completeness of preferences is required. The assumption made by Mount and Reiter (1975) of the existence of an E-threshold is also not required here. These results are possible due to properties of the order topology introduced in Chichilnisky (1977). As we shall now discuss, this topology has quite desirable features for the study of preferences, and these now make it a natural choice for the problem at hand.
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- Mount, Kenneth R. & Reiter, Stanley, 1976.
"Construction of a continuous utility function for a class of preferences,"
Journal of Mathematical Economics,
Elsevier, vol. 3(3), pages 227-245, December.
- Kenneth R. Mount & Stanley Reiter, 1975. "Construction of a Continuous Utility Function for a Class of Preferences," Discussion Papers 170, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Chichilnisky, Graciela, 1977. "Spaces of economic agents," Journal of Economic Theory, Elsevier, vol. 15(1), pages 160-173, June.
- Hildenbrand, Werner, 1970. "On economies with many agents," Journal of Economic Theory, Elsevier, vol. 2(2), pages 161-188, June.
- Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
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