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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A functional equation arising from ranked additive and separable utility


Authors: János Aczél, Gyula Maksa, Che Tat Ng and Zsolt Páles
Journal: Proc. Amer. Math. Soc. 129 (2001), 989-998
MSC (2000): Primary 39B12, 39B22, 39B72; Secondary 26A48, 26A51, 91A30, 91C05
Published electronically: October 4, 2000
MathSciNet review: 1814138
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Abstract | References | Similar Articles | Additional Information

Abstract:

All strictly monotonic solutions of a general functional equation are determined. In a particular case, which plays an essential role in the axiomatization of rank-dependent expected utility, all nonnegative solutions are obtained without any regularity conditions. An unexpected possibility of reduction to convexity makes the present proof possible.


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Additional Information

János Aczél
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Address at time of publication: Institute for Mathematical Behavioral Sciences, University of California, Irvine, California 92697-5100
Email: jdaczel@math.uwaterloo.ca, janos@aris.ss.uci.edu

Gyula Maksa
Affiliation: Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary
Email: maksa@math.klte.hu

Che Tat Ng
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: ctng@math.uwaterloo.ca

Zsolt Páles
Affiliation: Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary
Email: pales@math.klte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05686-0
PII: S 0002-9939(00)05686-0
Keywords: Functional equation, binary gamble, rank-dependent expected utility, convexity
Received by editor(s): June 7, 1999
Published electronically: October 4, 2000
Additional Notes: This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada Grants OGP 0002972 and OGP 0008212, by the Hungarian National Science Foundation (OTKA) Grant T-030082 and by the Higher Education Research Council (FKFP) Grant 0310/1997.
The authors are grateful to R.\ Duncan Luce for communicating the problem and explanations and to the referee for pointing out a confusing misprint in the first version of the manuscript.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2000 American Mathematical Society