Center for Economic Research, Department of Economics, University of Minnesota
Representing binary ordering relations by numerical functions is a
basic problem of the theory of measurement. It has applications in many fields
of science, and arises in psychology and economics as the problem of establishing
utility functions for preference relations.
We obtain definable utility representations for (both continuous and upper
semicontinuous) definable preferences in o-minimal expansions of real closed ordered
fields. Such preferences have particular significance for modeling "bounded
rationality" . Our proofs are based on geometric theorems for definable sets,
and provide new alternatives to the classical tools of separability (Debreu ,
Rader ) and metric-completeness (Arrow and Hahn ).
The initial application of these ideas in economics was made by Blume and
Zame (1992). Our results extend their Theorem 1 in several directions (see
Remark la below).
Richter, M.K. and Wong, K., (1996), "Definable Utility in O-Minimal Structures", Discussion Paper No. 296, Center for Economic Research, Department of Economics, University of Minnesota.
Richter, Marcel K.; Wong, Kam-Chau.
Definable Utility in O-Minimal Structures.
Center for Economic Research, Department of Economics, University of Minnesota.
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