Single-Call Mechanisms

Truthfulness is fragile and demanding. It is oftentimes computationally harder than solving the original problem. 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 largely settle when and to what extent single-call mechanisms are possible. The first single-call construction was discovered by Babaioff, Kleinberg, and Slivkins [BKS10] 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 [BKS10]: 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 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 [BKS10] simultaneously optimize a variety of metrics in their respective domains. As an example, 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.