A functional equation arising from ranked additive and separable utility
نویسندگان
چکیده
منابع مشابه
A Functional Equation Arising from Ranked Additive and Separable Utility
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.
متن کاملSolution of a Functional Equation Arising from Utility That Is Both Separable and Additive
The problem of determining all utility measures over binary gambles that are both separable and additive leads to the functional equation f(v) = f(vw) + f [vQ(w)], v, vQ(w) ∈ [0, k), w ∈ [0, 1] . The following conditions are more or less natural to the problem: f strictly increasing, Q strictly decreasing; both map their domains onto intervals (f onto a [0, K), Q onto [0, 1]); thus both are con...
متن کاملRanked Additive Utility Representations of Gambles: Old and New Axiomatizations
A number of classical as well as quite new utility representations for gains are explored with the aim of understanding the behavioral conditions that are necessary and sufficient for various subfamilies of successively stronger representations to hold. Among the utility representations are: ranked additive, weighted, rank-dependent (which includes cumulative prospect theory as a special case),...
متن کاملOn a Functional Equation Arising from a Queueing Model
Functional equations play an important role in many applications. They offer a powerful tool for narrowing the models used to describe many phenomena. In particular, a certain challenging class of functional equations arises recently from many applications like e.g. networks and databases. Usually, such class of equations stems when obtaining the generating functions of queueing systems distrib...
متن کاملReconsidering a functional equation arising from number theory
In a recent paper Chávez and Sahoo considered the functional equation f(ux− vy, uy + v(x+ y)) = f(x, y)f(u, v), which arose in a number theoretical context. Unfortunately one of their results is incorrect. Here we reconsider the equation on various domains. We observe that it is in fact a multiplicative Cauchy equation in disguise. We also point out some remaining open problems.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05686-0