Abstract
We study the trade-off between the Price of Anarchy (PoA) and the Price of Stability (PoS) in mechanism design, in the prototypical problem of unrelated machine scheduling. We give bounds on the space of feasible mechanisms with respect to the above metrics, and observe that two fundamental mechanisms, namely the First-Price (FP) and the Second-Price (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous task-independent mechanisms, we completely characterize the PoA/PoS Pareto frontier; we design a class of optimal mechanisms \(\mathcal {SP}_\alpha \) that lie exactly on this frontier. In particular, these mechanisms range smoothly, with respect to parameter \(\alpha \ge 1\) across the frontier, between the First-Price (\(\mathcal {SP}_1\)) and Second-Price (\(\mathcal {SP}_\infty \)) mechanisms.
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