Strong Nash equilibria and Pareto-optimal Nash equilibria are natural and important strengthenings of the Nash equilibrium concept. We study these stronger notions of equilibrium in congestion games, focusing on the relationships between the price of anarchy for these equilibria and that for standard Nash equilibria (which is well understood). For symmetric congestion games with polynomial or exponential latency functions, we show that the price of anarchy for strong and Pareto-optimal equilibria is much smaller than the standard price of anarchy. On the other hand, for asymmetric congestion games with polynomial latencies the strong and Pareto prices of anarchy are essentially as large as the standard price of anarchy; while for asymmetric games with exponential latencies the Pareto and standard prices of anarchy are the same but the strong price of anarchy is substantially smaller. Finally, in the special case of linear latencies, we show that the strong and Pareto prices of anarchy coincide exactly with the known value 5/2 for standard Nash, but are strictly smaller for symmetric games.

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