## Abstract

We consider the problem of designing mechanisms that interact with strategic agents through strategic intermediaries (or mediators), and investigate the cost to society due to the mediators' strategic behavior. Selfish agents with private information are each associated with exactly one strategic mediator, and can interact with the mechanism exclusively through that mediator. Each mediator aims to optimize the combined utility of his agents, while the mechanism aims to optimize the combined utility of all agents. We focus on the problem of facility location on a metric induced by a publicly known tree. With non-strategic mediators, there is a dominant strategy mechanism that is optimal. We show that when both agents and mediators act strategically, there is no dominant strategy mechanism that achieves any approximation. We, thus, slightly relax the incentive constraints, and define the notion of a two-sided incentive compatible mechanism. We show that the 3-competitive deterministic mechanism suggested by Procaccia and Tennenholtz [12] and Dekel et al. [3] for lines extends naturally to trees, and is still 3-competitive as well as two-sided incentive compatible. This is essentially the best possible [3, 12]. We then show that by allowing randomization one can construct a 2-competitive randomized mechanism that is two-sided incentive compatible, and this is also essentially tight. This result also closes a gap left in the work of Procaccia and Tennenholtz [12] and Lu et al. [8] for the simpler problem of designing strategy-proof mechanisms for weighted agents with no mediators on a line, while extending to the more general model of trees. We also investigate a further generalization of the above setting where there are multiple levels of mediators.

Original language | English |
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Title of host publication | ITCS 2015 - Proceedings of the 6th Innovations in Theoretical Computer Science |

Publisher | Association for Computing Machinery, Inc |

Pages | 307-316 |

Number of pages | 10 |

ISBN (Electronic) | 9781450333337 |

DOIs | |

State | Published - 11 Jan 2015 |

Externally published | Yes |

Event | 6th Conference on Innovations in Theoretical Computer Science, ITCS 2015 - Rehovot, Israel Duration: 11 Jan 2015 → 13 Jan 2015 |

### Publication series

Name | ITCS 2015 - Proceedings of the 6th Innovations in Theoretical Computer Science |
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### Conference

Conference | 6th Conference on Innovations in Theoretical Computer Science, ITCS 2015 |
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Country/Territory | Israel |

City | Rehovot |

Period | 11/01/15 → 13/01/15 |

### Bibliographical note

Publisher Copyright:Copyright © 2015 ACM.

## Keywords

- Facility location
- Mechanism design
- Mediators

## ASJC Scopus subject areas

- Computational Theory and Mathematics