# Definition:Utility Function

## Definition

Let $G$ be a game.

Let $P$ be a player of $G$.

Let $C$ be the set $C$ of consequences of the moves available to $P$.

A utility function on $C$ is a mapping from $C$ to the real numbers $\R$ so as to define a preference relation on $C$:

$U: C \to \R$

by the condition:

$\forall x, y \in C: x \succsim y \iff \map U x \ge \map U y$