Fair Interventions in Weighted Congestion Games
CoRR(2023)
摘要
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 the sense
that identical players receive identical treatment. 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 propose a taxation mechanism that is fair and show that the
resulting price of anarchy matches this lower bound, while the mechanism can be
efficiently computed in polynomial time. Third, we complement these results by
showing 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 approximate below a factor identical to the one
previously introduced. In doing so, we also show that the randomized algorithm
proposed by Makarychev and Sviridenko (Journal of the ACM, 2018) for the class
of 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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