A functional equation arising from simultaneous utility representations
type: Item
instance of: scholarly article
title: A functional equation arising from simultaneous utility representations
zbMATH Open document ID: 1041.39015
DOI: 10.1007/BF03322735
author: R. Duncan Luce
author: János Aczél
author: A. A. J. Marley
published in: Results in Mathematics
publication date: 2003-10-29T00:00:00Z
review text: This paper works out consequences of assuming that two families of utility preferences, one additive and the other of increasing increments, hold simultaneously for a class of binary gambles. The assumption leads to the functional equation \[ f[h(x-y)+y]=f[h(x)]-f[h(y)]+f(y) \] for \(0\leq y\leq x<\kappa \), and the inequality \(h(x)\leq x\) for \(0\leq x\leq \kappa \), for strictly increasing functions \(f,h\) on a real interval \([0,\kappa [ \). The authors find all differentiable solutions. An open problem is to find all solutions without assuming differentiability.
reviewed by: Bruce Ebanks
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 91A30
zbMATH DE Number: 1997681
zbMATH Keywords: functional equation
zbMATH Keywords: utility representations
zbMATH Keywords: binary gambles
zbMATH Keywords: differentiable solution
MaRDI profile type: Publication
cites work: Q5514010
cites work: Increasing increment generalizations of rank-dependent theories
cites work: Ranked additive utility representations of gambles: Old and new axiomatizations
full work available at URL: https://doi.org/10.1007/bf03322735
OpenAlex ID: W2160993604
description: scientific article; zbMATH DE number 1997681