Binary Relations and Choice Functions Representable via Utility Functions and Supermodular or Multiplicative Error Functions
✍ Scribed by Fuad Aleskerov; Yusufcan Masatlioglu
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 34 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
✦ Synopsis
The Choice functions rationalizable via utility functions and supermodular error functions depending on feasible set of alternatives are considered. It is shown that a very narrow class of choice functions can be represented in this form. To c haracterize that class of functions, a new class of binary relations -simple semiorders -is introduced. Binary relations which have numerical representation via utility functions and multiplicative error functions are studied. The classes of binary relations are found for the cases when the error function depends on the utility function in a di erent w ay, namely, when the error function is proportional to the utility function, and when the error function is inversely proportional to that function.