Truthful Mechanisms with Implicit Payment Computation

Abstract

It is widely believed that computing payments needed to induce truthful bidding is somehow harder than simply computing the allocation. We show that the opposite is true: creating a randomized truthful mechanism is essentially as easy as a single call to a monotone allocation rule. Our main result is a general procedure to take a monotone allocation rule for a single-parameter domain and transform it (via a black-box reduction) into a randomized mechanism that is truthful in expectation and individually rational for every realization. The mechanism implements the same outcome as the original allocation rule with probability arbitrarily close to 1, and requires evaluating that allocation rule only once. We also provide an extension of this result to multiparameter domains and cycle-monotone allocation rules, under mild star-convexity and nonnegativity hypotheses on the type space and allocation rule, respectively.Because our reduction is simple, versatile, and general, it has many applications to mechanism design problems in which re-evaluating the allocation rule is either burdensome or informationally impossible. Applying our result to the multiarmed bandit problem, we obtain truthful randomized mechanisms whose regret matches the information-theoretic lower bound up to logarithmic factors, even though prior work showed this is impossible for truthful deterministic mechanisms. We also present applications to offline mechanism design, showing that randomization can circumvent a communication complexity lower bound for deterministic payments computation, and that it can also be used to create truthful shortest path auctions that approximate the welfare of the VCG allocation arbitrarily well, while having the same running time complexity as Dijkstra's algorithm. This is a merged and revised version of the conference papers [Babaioff et al. 2010[Babaioff et al. , 2013b that appeared in the ACM Conference on Electronic Commerce (ACM EC) in 2010 and 2013, respectively. This article contains all results from Babaioff et al. [2010] and the main result from Babaioff et al. [2013b] (in Section 8). This version is updated to reflect the current status of the follow-up work and open questions.

Algorithms as Mechanisms

“…Our work is closely related to the literature on so-called "back-box reductions", which has led to some of the most impressive results in algorithmic mechanism design (such as [Lavi and Swamy 2005;Briest et al 2005;Dughmi and Roughgarden 2014;Dughmi et al 2011;Babaioff et al 2010Babaioff et al , 2013). This approach takes an algorithm, and aims to implement the algorithm's outcome via a game.…”

“…The main difference to our work is that standard rounding procedures are often oblivious but typically not convex. Babaioff et al [2010Babaioff et al [ , 2013 show how to transform a monotone or cycle-monotone algorithm into a truthful-in-expectation mechanism using a single call to the algorithm. The resulting mechanism coincides with the algorithm with high probability.…”

Sponsored Search Auctions

“…For example, Babaioff et al [2010] derived a regret bound for randomized MAB mechanism, which is truthful in expectation over random seeds and satisfies additional individual rational conditions. The lower bound for the regret is (T 1/2 ), which matches the lower bound of MAB algorithms without truthful restrictions.…”

Smooth Online Mechanisms

“…Online pay-per-click advertising can also be formulated as an online mechanism design problem with uncertain supply; this application was addressed in [Babaioff et al 2009[Babaioff et al , 2010Devanur and Kakade 2009]. In these works the bidders don't have intertemporal preferences-their value is linear in the quantity of clicks they receive, irrespective of when those clicks are received-but the uncertainty of supply is treated with a more elaborate model: the availability of an item (a user's click) depends on the bidder to whom it is allocated, because a user may click one ad if it is shown, but not another.…”