Single-Call Mechanisms

Christopher A. Wilkens, Balasubramanian Sivan

Abstract: Truthfulness is fragile and demanding. It is oftentimes harder to guarantee truthfulness when solving a problem than it is to solve the problem itself. Even worse, truthfulness can be utterly destroyed by small uncertainties in a mechanism’s outcome. One obstacle is that truthful payments depend on outcomes other than the one realized, such as the lengths of non-shortest-paths in a shortest-path auction. Single-call mechanisms are a powerful tool that circumvents this obstacle: they implicitly charge truthful payments, guaranteeing truthfulness in expectation using only the outcome realized by the mechanism. The cost of such truthfulness is a trade-off between the expected quality of the outcome and the risk of large payments. We study two of the most general domains for truthful mechanisms and largely settle when and to what extent single-call mechanisms are possible. The first single-call construction was discovered by Babaioff et al. [2010] in single-parameter domains. They give a transformation that turns any monotone, single-parameter allocation rule into a truthful-in-expectation single-call mechanism. Our first result is a natural complement to Babaioff et al. [2010]: we give a new transformation that produces a single-call VCG mechanism from any allocation rule for which VCG payments are truthful. Second, in both the single-parameter and VCG settings, we precisely characterize the possible transformations, showing that a wide variety of transformations are possible but that all take a very simple form. Finally, we study the inherent trade-off between the expected quality of the outcome and the risk of large payments. We show that our construction and that of Babaioff et al. [2010] simultaneously optimize a variety of metrics in their respective domains. Our study is motivated by settings where uncertainty in a mechanism renders other known techniques untruthful, and we offer a variety of examples where such uncertainty can arise. In particular, we analyze pay-per-click advertising auctions, where the truthfulness of the standard VCG-based auction is easily broken when the auctioneer’s estimated click-through-rates are imprecise.