An operational test for existence of a consistent increasing quasi-concave value function

TL;DR

This paper develops a practical test to determine the existence of a consistent increasing quasi-concave value function based on given preferences, with applications across economics and decision making.

Contribution

It provides necessary and sufficient conditions for existence and constructs methods for creating consistent linear and non-linear value functions.

Findings

Established an operational test for value function existence.

Derived necessary and sufficient conditions for the existence of such functions.

Constructed methods for linear and non-linear value functions.

Abstract

Existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. In this paper, we establish necessary and sufficient conditions for existence of a value function satisfying aforementioned properties. This leads to an operational, tractable and easy to use test for checking the existence of a desirable value function. In addition to developing the existence test, we construct consistent linear and non-linear desirable value functions.