### Abstract

We revisit the well-studied problem of designing mechanisms for one-sided matching markets, where a set of n agents needs to be matched to a set of n heterogeneous items. Each agent i has a value v_{i,j} for each item j, and these values are private information that the agents may misreport if doing so leads to a preferred outcome. Ensuring that the agents have no incentive to misreport requires a careful design of the matching mechanism, and mechanisms proposed in the literature mitigate this issue by eliciting only the ordinal preferences of the agents, i.e., their ranking of the items from most to least preferred. However, the efficiency guarantees of these mechanisms are based only on weak measures that are oblivious to the underlying values. In this paper we achieve stronger performance guarantees by introducing a mechanism that truthfully elicits the full cardinal preferences of the agents, i.e., all of the v_{i,j} values. We evaluate the performance of this mechanism using the much more demanding Nash bargaining solution as a benchmark, and we prove that our mechanism significantly outperforms all ordinal mechanisms (even non-truthful ones). To prove our approximation bounds, we also study the population monotonicity of the Nash bargaining solution in the context of matching markets, providing both upper and lower bounds which are of independent interest.

Original language | English (US) |
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Title of host publication | 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 |

Editors | Shuchi Chawla |

Publisher | Association for Computing Machinery |

Pages | 2096-2113 |

Number of pages | 18 |

ISBN (Electronic) | 9781611975994 |

State | Published - 2020 |

Event | 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, United States Duration: Jan 5 2020 → Jan 8 2020 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 2020-January |

### Conference

Conference | 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 |
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Country | United States |

City | Salt Lake City |

Period | 1/5/20 → 1/8/20 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020*(pp. 2096-2113). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2020-January). Association for Computing Machinery.