## Abstract

We provide a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for problems with multidimensional and continuous type spaces. The key technical barrier preventing exact incentive compatibility in prior black-box reductions is that repairing violations of incentive constraints requires understanding the distribution of the mechanism's output, which is typically #P-hard to compute. Reductions that instead estimate the output distribution by sampling inevitably suffer from sampling error, which typically precludes exact incentive compatibility. We overcome this barrier by employing and generalizing the computational model in the literature on Bernoulli Factories. In a Bernoulli factory problem, one is given a function mapping the bias of an "input coin" to that of an "output coin", and the challenge is to efficiently simulate the output coin given only sample access to the input coin. Consider a generalization which we call the expectations from samples computational model, in which a problem instance is specified by a function mapping the expected values of a set of input distributions to a distribution over outcomes. The challenge is to give a polynomial time algorithm that exactly samples from the distribution over outcomes given only sample access to the input distributions. In this model, we give a polynomial time algorithm for the function given by exponential weights: expected values of the input distributions correspond to the weights of alternatives and we wish to select an alternative with probability proportional to an exponential function of its weight. This algorithm is the key ingredient in designing an incentive compatible mechanism for bipartite matching, which can be used to make the approximately incentive compatible reduction of Hartline et al. [12] exactly incentive compatible.

Original language | English (US) |
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Title of host publication | STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Pierre McKenzie, Valerie King, Hamed Hatami |

Publisher | Association for Computing Machinery |

Pages | 158-169 |

Number of pages | 12 |

ISBN (Electronic) | 9781450345286 |

DOIs | |

State | Published - Jun 19 2017 |

Event | 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 - Montreal, Canada Duration: Jun 19 2017 → Jun 23 2017 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F128415 |

ISSN (Print) | 0737-8017 |

### Other

Other | 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 |
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Country | Canada |

City | Montreal |

Period | 6/19/17 → 6/23/17 |

## Keywords

- BIC reduction
- Bayesian mechanism design
- Bernoulli factory
- Online convex programming

## ASJC Scopus subject areas

- Software