The Pareto Frontier of Inefficiency in Mechanism Design
Abstract
We study the tradeoff 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 FirstPrice (FP) and the SecondPrice (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous taskindependent 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 $\alpha\geq 1$ across the frontier, between the FirstPrice ($\mathcal{SP}_1$) and SecondPrice ($\mathcal{SP}_\infty$) mechanisms. En route to these results, we also provide a definitive answer to an important question related to the scheduling problem, namely whether nontruthful mechanisms can provide better makespan guarantees in the equilibrium, compared to truthful ones. We answer this question in the negative, by proving that the Price of Anarchy of all scheduling mechanisms is at least $n$, where $n$ is the number of machines.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.03454
 Bibcode:
 2018arXiv180903454F
 Keywords:

 Computer Science  Computer Science and Game Theory
 EPrint:
 To be published in Mathematics of Operations Research