Abstract

We give the first black-box reduction from approximation algorithms to truthful approximation mechanisms for a non-trivial class of multi-parameter problems. Specifically, we prove that every welfare-maximization problem that admits a fully polynomial-time approximation scheme (FPTAS) and can be encoded as a packing problem also admits a truthful-in-expectation randomized mechanism that is an FPTAS. Our reduction makes novel use of smoothed analysis by employing small perturbations as a tool in algorithmic mechanism design. We develop a “duality” between linear perturbations of the objective function of an optimization problem and of its feasible set, and we use the “primal” and “dual” viewpoints to prove the running time bound and the truthfulness guarantee, respectively, for our mechanism.

Keywords

  1. algorithmic mechanism design
  2. smoothed analysis
  3. black-box reductions

MSC codes

  1. 68Q25
  2. 91A99

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 312 - 336
ISSN (online): 1095-7111

History

Submitted: 8 August 2011
Accepted: 5 August 2013
Published online: 20 February 2014

Keywords

  1. algorithmic mechanism design
  2. smoothed analysis
  3. black-box reductions

MSC codes

  1. 68Q25
  2. 91A99

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