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arXiv · 2311.16760

Fair Interventions in Weighted Congestion Games

Miriam Fischer·Martin Gairing·Dario Paccagnan
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Abstract

In this work we study the power and limitations of fair interventions in weighted congestion games. Specifically, we focus on interventions that aim at improving the equilibrium quality (price of anarchy) and are fair in a suitably defined sense. Within this setting, we provide three key contributions. First, we show that no fair intervention can reduce the price of anarchy below a given factor depending solely on the class of latencies considered. Interestingly, this lower bound is unconditional, i.e., it applies regardless of how much computation interventions are allowed to use. Second, we design a taxation mechanism that is fair and achieves a price of anarchy matching this unconditional lower bound, all the while being polynomial-time computable. Third, we show that no intervention (fair or not) can achieve a better approximation if polynomial computability is required. We do so by proving that the minimum social cost is NP-hard to minimize below a factor identical to the one previously introduced. In doing so, our work shows that the algorithm proposed by Makarychev and Sviridenko (Journal of the ACM, 2018) to tackle optimization problems with a "diseconomy of scale" is optimal, and provide a novel way to derandomize its solution via equilibrium computation.

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Miriam Fischer, Martin Gairing, Dario Paccagnan. 2023-11-28. Fair Interventions in Weighted Congestion Games. https://arxiv.org/abs/2311.16760

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