Truthful Mechanisms with Implicit Payment Computation
- Moshe Babaioff ,
- Robert Kleinberg ,
- Aleksandrs Slivkins
ACM Conference on Electronic Commerce (EC'10) |
Published by Association for Computing Machinery, Inc.
Best Paper Award (ACM EC 2010). The full version can be found on arxiv.org (http://arxiv.org/abs/1004.3630).
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 for single-parameter domains: creating a randomized truthful mechanism is essentially as easy as a single call to a monotone allocation function. Our main result is a general procedure to take a monotone allocation rule and transform it (via a black-box reduction) into a randomized mechanism that is truthful in expectation and individually rational for every realization. Moreover, 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.
Because our reduction is simple, versatile, and general, it has many applications to mechanism design problems in which re-evaluating the allocation function is either burdensome or informationally impossible. Applying our result to the truthful multi-armed bandit problem, we obtain randomized mechanisms whose regret matches the information-theoretic lower bound up to logarithmic factors, even though prior work showed this is impossible for 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.
Best Paper Award (ACM EC 2010).
Copyright © 2007 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or firstname.lastname@example.org. The definitive version of this paper can be found at ACM's Digital Library --http://www.acm.org/dl/.