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The averaging principle

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 $O(ε^2)$ equivalent to the outcome of the corresponding homogeneous model, where $ε$ 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).