Duality between direct and indirect preferences
This paper develops a duality theory for preference orders, and highlights important differences with respect to the cardinal utility approach. Our main result is a symmetric duality theorem, under the minimal hypotheses, between direct and indirect preferences. In contrast to the cardinal theory, we also find that these conditions do not completely characterize the class of indirect preference orders.
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- Crouzeix, J. P.: Duality between direct and indirect utility functions: differentiability properties. J. Math. Econ.12, 149–165 (1983)Google Scholar
- Diewert, W. E.: Duality approaches to microeconomic theory. In: Arrow, K. J., Intriligator, M. D. (eds.) Handbook of Mathematical Economics, vol. 2, pp. 535–599. Amsterdam: North-Holland 1982Google Scholar
- Fenchel, W.: A remark on convex sets and polarity. Comm. Sem. Math. Univ. Lund (Medd. Lunds Univ. Math. Sem.) Tome Supplém., 82–89 (1952)Google Scholar
- Martinez-Legaz, J.-E.: Quasiconvex duality theory by generalized conjugation methods. Optimization19, 603–652 (1988)Google Scholar
- Martinez-Legaz, J.-E.: Duality between direct and indirect utility functions under minimal hypotheses. J. Math. Econ.20, 199–209 (1991)Google Scholar
- Szász, G.: Introduction to lattice theory. Cambridge: Cambridge University Press (1963)Google Scholar
- Yannelis, N. C., Prabhakar, N. D.: Existence of maximal elements and equilibria in linear topological spaces. J. Math. Econ.12, 233–245 (1983)Google Scholar