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This work focuses on the design of taxes in atomic congestion games, acommonly studied model for competitive resource sharing. While most relatedstudies focus on optimizing either the worst- or best-case performance (i.e.,Price of Anarchy (PoA) or Price of Stability (PoS)), we investigate whetheroptimizing for the PoA has consequences on the PoS. Perhaps surprisingly, ourresults reveal a fundamental trade-off between the two performance metrics. Ourmain result demonstrates that the taxation rule that optimizes the PoA inheritsa matching PoS, implying that the best outcome is no better than the worstoutcome under such a design choice. We then study this trade-off in terms ofthe Pareto frontier between the PoA and PoS. Our results also establish thatany taxes with PoS equal to 1 incur a much higher PoA, and that, in severalwell-studied cases, the untaxed setting lies strictly above the Paretofrontier.

The Unintended Consequences of Minimizing the Price of Anarchy in Congestion Games