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