Results 1 
3 of
3
On the Limits of BlackBox Reductions in Mechanism Design
"... We consider the problem of converting an arbitrary approximation algorithm for a singleparameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are blackbox, meaning that they require only oracle access to the given algorithm and in particular ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
(Show Context)
We consider the problem of converting an arbitrary approximation algorithm for a singleparameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are blackbox, meaning that they require only oracle access to the given algorithm and in particular do not require explicit knowledge of the problem constraints. Such a reduction is known to be possible, for example, for the social welfare objective when the goal is to achieve Bayesian truthfulness and preserve social welfare in expectation. We show that a blackbox reduction for the social welfare objective is not possible if the resulting mechanism is required to be truthful in expectation and to preserve the worstcase approximation ratio of the algorithm to within a subpolynomial factor. Further, we prove that for other objectives such as makespan, no blackbox reduction is possible even if we only require Bayesian truthfulness and an averagecase performance guarantee.
BlackBox Reductions for CostSharing Mechanism Design
"... We consider the design of strategyproof costsharing mechanisms. We give two simple, but extremely versatile, blackbox reductions, that in combination reduce the costsharing mechanismdesign problem to the algorithmic problem of finding a minimumcost solution for a set of players. Our first reduc ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We consider the design of strategyproof costsharing mechanisms. We give two simple, but extremely versatile, blackbox reductions, that in combination reduce the costsharing mechanismdesign problem to the algorithmic problem of finding a minimumcost solution for a set of players. Our first reduction shows that any truthful, αapproximation mechanism for the socialcost minimization (SCM) problem satisfying a technical nobossiness condition can be morphed into a truthful mechanism that achieves an O(α log n)approximation where the prices recover the cost incurred. Thus, we decouple the task of truthfully computing an outcome with nearoptimal social cost from the costsharing problem. This is fruitful since truthful mechanismdesign, especially for singledimensional problems, is a relatively wellunderstood and manageable task. Our second reduction nicely complements the first one by showing that any LPbased ρapproximation for the problem of finding a mincost solution for a set of players yields a truthful, nobossy, (ρ + 1)approximation for the SCM problem (and hence, a truthful (ρ + 1) log napproximation costsharing mechanism). These reductions find a slew of applications, yielding, as corollaries, the first or improved polytime costsharing mechanisms for a variety of problems. For example, our first reduction coupled with the celebrated VCG mechanism shows that for any costsharing problem (with a monotone cost function) one can obtain a truthful mechanism that achieves an O(log n)approximation where the prices recover the cost incurred. Other applications include O(log n)approximation mechanisms for: survivable network design problems, facility location (FL) problems including capacitated and connected FL problems, and minimummakespan scheduling on unrelated machines. Our results demonstrate that in contrast with our current understanding of groupstrategyproof and acyclic mechanisms, strategyproofness allows for ample flexibility in costsharing mechanism design enabling one to effectively leverage various algorithmic results.
BlackBox Reductions for CostSharing Mechanism
"... We consider the design of strategyproof costsharing mechanisms. We give two simple, but extremely versatile, blackbox reductions, that in combination reduce the costsharing mechanismdesign problem to the algorithmic problem of finding a mincost solution for a set of players. Our first reductio ..."
Abstract
 Add to MetaCart
We consider the design of strategyproof costsharing mechanisms. We give two simple, but extremely versatile, blackbox reductions, that in combination reduce the costsharing mechanismdesign problem to the algorithmic problem of finding a mincost solution for a set of players. Our first reduction shows that any truthful, αapproximation mechanism for the socialcost minimization (SCM) problem satisfying a technical nobossiness condition can be morphed into a truthful mechanism that achieves an O(α log n)approximation where the prices recover the cost incurred. Thus, we decouple (modulo nobossiness) the task of truthfully computing an outcome with nearoptimal social cost from the costsharing problem. This is fruitful since truthful mechanismdesign, especially for singledimensional problems, is a relatively wellunderstood and manageable task. Our second reduction nicely complements the first one by showing that any LPrelative ρapproximation for the problem of finding a mincost solution for a set of players yields a truthful, nobossy, (ρ+ 1)approximation for the SCM problem (and hence, a truthful (ρ + 1) log napproximation costsharing mechanism).