Existence of Utility Function

utility-theory

Definition

Existence of Utility Function

Given an agent’s preferences that satisfy the axioms of utility theory, there exists a real-valued function $U$ such that:

$$\begin{array}{rl}U(A)>U(B)& ⟺A\succ B\\ U(A)=U(B)& ⟺A\sim B\end{array}$$