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Potential functions and the inefficiency of equilibria

We survey one area of the emerging field of algorithmic game theory: the use of
approximation measures to quantify the inefficiency of game-theoretic equilibria. Potential
functions, which enable the application of optimization theory to the study of equilibria, have been
a versatile and powerful tool in this area. We use potential functions to bound the inefficiency of
equilibria in three diverse, natural classes of games: selfish routing networks, resource allocation
games, and Shapley network design games.