### Abstract

MC-nets is a concise representation of the characteristic functions that exploits a set of rules to compute payoffs. Given aMC-nets instance, the problem of computing a payoff division in the least core, which is a generalization of the core-non-emptiness problem that is known to be coNP-complete, is definitely a hard computational problem. In fact, to the best of our knowledge, no algorithm can actually compute such a payoff division for MC-nets instances with dozens of agents. We propose a new algorithm for this problem, that exploits the constraint generation technique to solve the linear programming problem that potentially has a huge number of constraints. Our experimental results are striking since, using 8 GB memory, our proposed algorithm can successfully compute a payoff division in the least core for the instances with up to 100 agents, but the naive algorithm fails due to a lack of memory for instances with 30 or more agents.

Original language | English |
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Title of host publication | PRIMA 2014 |

Subtitle of host publication | Principles and Practice of Multi-Agent Systems - 17th International Conference, Proceedings |

Editors | Yang Xu, Jeremy Pitt, Hoa Khanh Dam, Guido Governatori, Takayuki Ito |

Publisher | Springer Verlag |

Pages | 319-332 |

Number of pages | 14 |

ISBN (Electronic) | 9783319131900 |

Publication status | Published - Jan 1 2014 |

Event | 17th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2014 - Gold Coast, Australia Duration: Dec 1 2014 → Dec 5 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8861 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2014 |
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Country | Australia |

City | Gold Coast |

Period | 12/1/14 → 12/5/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*PRIMA 2014: Principles and Practice of Multi-Agent Systems - 17th International Conference, Proceedings*(pp. 319-332). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8861). Springer Verlag.

**Computing a payoff division in the least core for MC-nets coalitional games.** / Hirayama, Katsutoshi; Hanada, Kenta; Ueda, Suguru; Yokoo, Makoto; Iwasaki, Atsushi.

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

*PRIMA 2014: Principles and Practice of Multi-Agent Systems - 17th International Conference, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8861, Springer Verlag, pp. 319-332, 17th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2014, Gold Coast, Australia, 12/1/14.

}

TY - GEN

T1 - Computing a payoff division in the least core for MC-nets coalitional games

AU - Hirayama, Katsutoshi

AU - Hanada, Kenta

AU - Ueda, Suguru

AU - Yokoo, Makoto

AU - Iwasaki, Atsushi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - MC-nets is a concise representation of the characteristic functions that exploits a set of rules to compute payoffs. Given aMC-nets instance, the problem of computing a payoff division in the least core, which is a generalization of the core-non-emptiness problem that is known to be coNP-complete, is definitely a hard computational problem. In fact, to the best of our knowledge, no algorithm can actually compute such a payoff division for MC-nets instances with dozens of agents. We propose a new algorithm for this problem, that exploits the constraint generation technique to solve the linear programming problem that potentially has a huge number of constraints. Our experimental results are striking since, using 8 GB memory, our proposed algorithm can successfully compute a payoff division in the least core for the instances with up to 100 agents, but the naive algorithm fails due to a lack of memory for instances with 30 or more agents.

AB - MC-nets is a concise representation of the characteristic functions that exploits a set of rules to compute payoffs. Given aMC-nets instance, the problem of computing a payoff division in the least core, which is a generalization of the core-non-emptiness problem that is known to be coNP-complete, is definitely a hard computational problem. In fact, to the best of our knowledge, no algorithm can actually compute such a payoff division for MC-nets instances with dozens of agents. We propose a new algorithm for this problem, that exploits the constraint generation technique to solve the linear programming problem that potentially has a huge number of constraints. Our experimental results are striking since, using 8 GB memory, our proposed algorithm can successfully compute a payoff division in the least core for the instances with up to 100 agents, but the naive algorithm fails due to a lack of memory for instances with 30 or more agents.

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UR - http://www.scopus.com/inward/citedby.url?scp=84910144738&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84910144738

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 319

EP - 332

BT - PRIMA 2014

A2 - Xu, Yang

A2 - Pitt, Jeremy

A2 - Dam, Hoa Khanh

A2 - Governatori, Guido

A2 - Ito, Takayuki

PB - Springer Verlag

ER -