On the Averaging Principle

TL;DR

This paper introduces an averaging principle showing that outcomes of heterogeneous models are approximately equal to their homogeneous counterparts, with errors of order epsilon squared, simplifying analysis across various fields.

Contribution

It establishes a general averaging principle for models with heterogeneous properties, providing a new theoretical tool for simplifying complex analyses.

Findings

Outcomes are O(ε^2) close to homogeneous models under differentiability and interchangeability.

Applied the averaging principle to queueing theory, game theory, and social networks.

Derived new results and simplified analyses in these fields.

Abstract

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 differentiability and 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 averaging principle to obtain new results in queueing theory, game theory (auctions), and social networks (marketing).