### Abstract

Cooperative matching games have drawn much interest partly because of the connection with bargaining solutions in the networking environment. However, it is not always guaranteed that a network under investigation gives rise to a stable bargaining outcome. To address this issue, we consider a modification process, called stabilization, that yields a network with stable outcomes, where the modification should be as small as possible. Therefore, the problem is cast to a combinatorial-optimization problem in a graph. Recently, the stabilization by edge removal was shown to be NP-hard. On the contrary, in this paper, we show that other possible ways of stabilization, namely, edge addition, vertex removal and vertex addition, are all polynomial-time solvable. Thus, we obtain a complete complexity-theoretic classification of the natural four variants of the network stabilization problem. We further study weighted variants and prove that the variants for edge addition and vertex removal are NP-hard.

Original language | English |
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Title of host publication | AAMAS 2016 - Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems |

Publisher | International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS) |

Pages | 41-49 |

Number of pages | 9 |

ISBN (Electronic) | 9781450342391 |

Publication status | Published - Jan 1 2016 |

Event | 15th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2016 - Singapore, Singapore Duration: May 9 2016 → May 13 2016 |

### Publication series

Name | Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS |
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ISSN (Print) | 1548-8403 |

ISSN (Electronic) | 1558-2914 |

### Other

Other | 15th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2016 |
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Country | Singapore |

City | Singapore |

Period | 5/9/16 → 5/13/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Software
- Control and Systems Engineering

### Cite this

*AAMAS 2016 - Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems*(pp. 41-49). (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

**Efficient stabilization of cooperative matching games.** / Ito, Takehiro; Kakimura, Naonori; Kamiyama, Naoyuki; Kobayashi, Yusuke; Okamoto, Yoshio.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AAMAS 2016 - Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems.*Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS, International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), pp. 41-49, 15th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2016, Singapore, Singapore, 5/9/16.

}

TY - GEN

T1 - Efficient stabilization of cooperative matching games

AU - Ito, Takehiro

AU - Kakimura, Naonori

AU - Kamiyama, Naoyuki

AU - Kobayashi, Yusuke

AU - Okamoto, Yoshio

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Cooperative matching games have drawn much interest partly because of the connection with bargaining solutions in the networking environment. However, it is not always guaranteed that a network under investigation gives rise to a stable bargaining outcome. To address this issue, we consider a modification process, called stabilization, that yields a network with stable outcomes, where the modification should be as small as possible. Therefore, the problem is cast to a combinatorial-optimization problem in a graph. Recently, the stabilization by edge removal was shown to be NP-hard. On the contrary, in this paper, we show that other possible ways of stabilization, namely, edge addition, vertex removal and vertex addition, are all polynomial-time solvable. Thus, we obtain a complete complexity-theoretic classification of the natural four variants of the network stabilization problem. We further study weighted variants and prove that the variants for edge addition and vertex removal are NP-hard.

AB - Cooperative matching games have drawn much interest partly because of the connection with bargaining solutions in the networking environment. However, it is not always guaranteed that a network under investigation gives rise to a stable bargaining outcome. To address this issue, we consider a modification process, called stabilization, that yields a network with stable outcomes, where the modification should be as small as possible. Therefore, the problem is cast to a combinatorial-optimization problem in a graph. Recently, the stabilization by edge removal was shown to be NP-hard. On the contrary, in this paper, we show that other possible ways of stabilization, namely, edge addition, vertex removal and vertex addition, are all polynomial-time solvable. Thus, we obtain a complete complexity-theoretic classification of the natural four variants of the network stabilization problem. We further study weighted variants and prove that the variants for edge addition and vertex removal are NP-hard.

UR - http://www.scopus.com/inward/record.url?scp=85014285231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014285231&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85014285231

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 41

EP - 49

BT - AAMAS 2016 - Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems

PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)

ER -