Preference Symmetries, Partial Differential Equations, and Functional Forms for Utility
A discrete symmetry of a preference relation is a mapping from the domain of choice to itself under which preference comparisons are invariant; a continuous symmetry is a one-parameter family of such transformations that includes the identity; and a symmetry field is a vector field whose trajectories generate a continuous symmetry. Any continuous symmetry of a preference relation implies that its representations satisfy a system of PDEs. Conversely the system implies the continuous symmetry if the latter is generated by a field. Moreover, solving the PDEs yields the functional form for utility equivalent to the symmetry. This framework is shown to encompass a variety of representation theorems related to univariate separability, multivariate separability, and homogeneity, including the cases of Cobb-Douglas and CES utility.
|Date of creation:||Apr 2013|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +44 (0) 20 7882 5096
Fax: +44 (0) 20 8983 3580
Web page: http://www.econ.qmul.ac.uk
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004.
"Ambiguity Aversion, Robustness, and the Variational Representation of Preferences,"
Carlo Alberto Notebooks
12, Collegio Carlo Alberto, revised 2006.
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
- Mas-Colell, Andreu, 1977. "Regular, Nonconvex Economies," Econometrica, Econometric Society, vol. 45(6), pages 1387-1407, September.
- Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-32, July.
- Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002.
"Certainty Independence and the Separation of Utility and Beliefs,"
ICER Working Papers - Applied Mathematics Series
40-2002, ICER - International Centre for Economic Research.
- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January.
- Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
- Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
- Peter C. Fishburn, 1968. "Utility Theory," Management Science, INFORMS, vol. 14(5), pages 335-378, January.
When requesting a correction, please mention this item's handle: RePEc:qmw:qmwecw:wp702. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Nick Vriend)
If references are entirely missing, you can add them using this form.