Abstract
We investigate verification and existence problems for prominent stability concepts in hedonic games with friends, enemies, and optionally with neutrals [8, 15]. We resolve several (long-standing) open questions [4, 15, 19, 22] and show that for friend-oriented preferences, under the friends and enemies model, it is coNP-complete to verify whether a given agent partition is (strictly) core stable, while under the friends, enemies, and neutrals model, it is NP-complete to determine whether an individual stable partition exists. We further look into natural restricted cases from the literature, such as when the friends and enemies relationships are symmetric, when the initial coalitions have bounded size, when the vertex degree in the friendship graph (resp. the union of friendship and enemy graph) is bounded, or when such graph is acyclic or close to being acyclic. We obtain a complete (parameterized) complexity picture regarding these cases.
| Original language | English |
|---|---|
| Pages (from-to) | 251-259 |
| Number of pages | 9 |
| Journal | Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS |
| Volume | 2023-May |
| State | Published - 1 Jan 2023 |
| Externally published | Yes |
| Event | 22nd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2023 - London, United Kingdom Duration: 29 May 2023 → 2 Jun 2023 |
Keywords
- Core stable
- Friends and enemies
- Hedonic games
- Individually stable
- Nash stable
- Parameterized complexity
ASJC Scopus subject areas
- Artificial Intelligence
- Software
- Control and Systems Engineering