Utility2 2002-07-24 20:37:08 2004-04-28 11:32:33 Definition utility utility function % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Utility is taken to be an absolute, accurate measurement of how desirable something is; in particular, it differs from money in three key ways. First, desire for it is linear (generally in economics and game \PMlinkescapetext{theory} a person with a lot of money receives less utility from an additional \PMlinkescapetext{fixed} amount of money than someone with very little money). Second, when modeling a \PMlinkescapetext{real} situation, utility should include all external \PMlinkescapetext{factors} (the happiness received from doing a good deed, for instance). Third, different people's utility is incomparable. It is meaningless to ask whether one person gets more utility from a situation than another person does. Utilities for a given person can be compared only to other utilities for that person. A utility function is a function which specifies how much utility a player gets for a particular outcome. It maps the space $S$ of all possible strategy profiles to $\mathbb{R}$.