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:

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

Also see

• Definition:Model of Rational Choice
• Definition:Rules of Game

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): utility function
• 1991: Roger B. Myerson: Game Theory ... (previous) ... (next): $1.2$ Basic Concepts of Decision Theory
• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $1.4$: Rational Behavior
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): utility function