Price of Stability in Polynomial Congestion Games

The price of anarchy (PoA) in congestion games has attracted a lot of research over the past decade. This has resulted in a thorough understanding of this concept. In contrast, the price of stability (PoS), which is an equally interesting concept, is much less understood. In this article, we consider congestion games with polynomial cost functions with nonnegative coefficients and maximum degree d. We give matching bounds for the PoS in such games—that is, our technique provides the exact value for any degree d. For linear congestion games, tight bounds were previously known. Those bounds hold even for the more restricted case of dominant equilibria, which may not exist. We give a separation result showing that this is not possible for congestion games with quadratic cost functions—in other words, the PoA for the subclass of games that admit a dominant strategy equilibrium is strictly smaller than the PoS for the general class.