Utility Functions

Utility Functions in Game Theory quantify players’ preferences over outcomes, assigning numerical values to reflect satisfaction or benefit.

Definition

A utility function $u:O\to \mathbb{R}$ maps outcomes $O$ to real numbers, where higher values indicate greater preference.

Examples

For a player choosing between $10 or $20, a simple utility might be $u(\mathrm{\$}10)=10$, $u(\mathrm{\$}20)=20$. Risk-averse players might use $u(x)=\sqrt{x}$.

Applications

Used in economics to model consumer choice, in negotiations to assess offers, and in games to predict strategies.