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

TL;DR

This paper explores the trade-off between optimizing the Price of Anarchy and Price of Stability in congestion games, revealing that improving one can worsen the other and highlighting fundamental limitations in tax-based resource sharing.

Contribution

It demonstrates a fundamental trade-off between PoA and PoS in congestion games and characterizes the Pareto frontier for taxation strategies.

Findings

Taxation rules optimizing PoA inherit a matching PoS.

Taxes with PoS=1 lead to higher PoA.

Untaxed settings often lie above the Pareto frontier.

Abstract

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.