  Typically, models with a heterogeneous property are considerably harder to
analyze than the corresponding homogeneous models, in which the heterogeneous
property is replaced with its average value. In this study we show that any
outcome of a heterogeneous model that satisfies the two properties of
\emph{differentiability} and \emph{interchangibility}, is $O(\epsilon^2)$
equivalent to the outcome of the corresponding homogeneous model, where
$\epsilon$ is the level of heterogeneity. We then use this \emph{averaging
principle} to obtain new results in queueing theory, game theory (auctions),
and social networks (marketing).
