The Tension Between Anarchy and Stability in Congestion Games.

Mechanism design for the coordination of multiagent systems involves influencing agents' local decision making rules in order to improve the system-level performance of the joint behaviour. While the majority of the existing literature on this topic pursues the optimization of the worst case performance (i.e., price of anarchy), exploring whether or not optimizing for the worst case has consequences on the best case performance (i.e., price of stability) remains an underdeveloped direction. In this manuscript, we address this question for the well-studied class of atomic congestion games. Perhaps surprisingly, our results establish that a fundamental tradeoff exists between these two measures of performance. We also characterize upper and lower bounds on the corresponding Pareto frontier between the price of anarchy and the price of stability. Interestingly, we show that the mechanism that optimizes the price of anarchy inherits a matching price of stability, implying that the best equilibrium is not necessarily any better than the worst equilibrium for such a design choice. Our results also demonstrate that mechanisms ensuring that the system optimum is an equilibrium (i.e., price of stability equal to 1) incur much higher price of anarchy, and suggest that the joint performance guarantees under no incentives do not even lie on the Pareto frontier.