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arXiv · 2107.06331

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

Rahul Chandan·Dario Paccagnan·Jason R. Marden
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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.

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Rahul Chandan, Dario Paccagnan, Jason R. Marden. 2021-07-13. The Unintended Consequences of Minimizing the Price of Anarchy in Congestion Games. https://arxiv.org/abs/2107.06331

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