On a functional equation arising from comparison of utility representations |
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| Authors: | Attila Gilá nyi,Che Tat Ng |
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| Affiliation: | a Institute of Mathematics, University of Debrecen, 4010 Debrecen, Pf. 12, Hungary
b Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 |
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| Abstract: | We solve the functional equation F1(t)−F1(t+s)=F2[F3(t)+F4(s)] for real functions defined on intervals, assuming that F2 is positive valued and strictly monotonic and that F3 is continuous. The equation arose from the equivalence problem of utility representations under assumptions of separability, homogeneity and segregation (e-distributivity). |
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| Keywords: | Functional equation Utility representation Binary gamble Convexity |
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