## Abstract

In the celebrated stable-matching problem, there are two sets of agents M and W, and the members of M only have preferences over the members of W and vice versa. It is usually assumed that each member of M and W is a single entity. However, there are many cases in which each member of M or W represents a team that consists of several individuals with common interests. For example, students may need to be matched to professors for their final projects, but each project is carried out by a team of students. Thus, the students first form teams, and the matching is between teams of students and professors. When a team is considered as an agent from M or W, it needs to have a preference order that represents it. A voting rule is a natural mechanism for aggregating the preferences of the team members into a single preference order. In this paper, we investigate the problem of strategic voting in the context of stable-matching of teams. Specifically, we assume that members of each team use the Borda rule for generating the preference order of the team. Then, the Gale-Shapley algorithm is used for finding a stable-matching, where the set M is the proposing side. We show that the single-voter manipulation problem can be solved in polynomial time, both when the team is from M and when it is from W. We show that the coalitional manipulation problem is computationally hard, but it can be solved approximately both when the team is from M and when it is from W.

Original language | English |
---|---|

Title of host publication | Algorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings |

Editors | Panagiotis Kanellopoulos, Maria Kyropoulou, Alexandros Voudouris |

Publisher | Springer Science and Business Media Deutschland GmbH |

Pages | 562-579 |

Number of pages | 18 |

ISBN (Print) | 9783031157134 |

DOIs | |

State | Published - 2022 |

Event | 15th International Symposium on Algorithmic Game Theory, SAGT 2022 - Colchester, United Kingdom Duration: 12 Sep 2022 → 15 Sep 2022 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 13584 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th International Symposium on Algorithmic Game Theory, SAGT 2022 |
---|---|

Country/Territory | United Kingdom |

City | Colchester |

Period | 12/09/22 → 15/09/22 |

### Bibliographical note

Publisher Copyright:© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

### Funding

This research has been partly supported by the Israel Science Foundation under grant 1958/20, by the EU Project TAILOR under grant 952215, and by the Ministry of Science, Technology & Space (MOST), Israel.

Funders | Funder number |
---|---|

European Commission | 952215 |

Ministry of Science, Technology and Space | |

Israel Science Foundation | 1958/20 |