A Functional Equation Arising from Simultaneous Utility Representations

Autor: R. Duncan Luce, János Aczél, A. A. J. Marley
Rok vydání: 2003
Předmět:
Zdroj: Results in Mathematics. 43:193-197
ISSN: 1420-9012
0378-6218
DOI: 10.1007/bf03322735
Popis: Suppose that two classes of utility representations of preferences, one additive and one increasing increments, hold simultaneously over uncertain binary alternatives (gambles). This assumption leads to the functional equation $$ f[h(x-y)+y]=f[h(x)]-f[h(y)]+f(y)\qquad (\kappa >x\geq y\geq 0), $$ and to the inequality h(z) ≤ z (z ∈ [0, κ[), where the functions ƒ and h are strictly increasing maps of the real interval [0, κ[ onto the real intervals [0, λ[ and [0, μ[, respectively, κ, λ, μ ∈]0, ∞]. We present all solutions under the additional assumption of (first-order) differentiability.
Databáze: OpenAIRE
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