### Abstract

This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well.

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

Pages (from-to) | 503-533 |

Number of pages | 31 |

Journal | Autonomous Agents and Multi-Agent Systems |

Volume | 32 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jul 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Artificial Intelligence

### Cite this

*Autonomous Agents and Multi-Agent Systems*,

*32*(4), 503-533. https://doi.org/10.1007/s10458-018-9386-z

**Coalition structure generation in cooperative games with compact representations.** / Ueda, Suguru; Iwasaki, Atsushi; Conitzer, Vincent; Ohta, Naoki; Sakurai, Yuko; Yokoo, Makoto.

Research output: Contribution to journal › Article

*Autonomous Agents and Multi-Agent Systems*, vol. 32, no. 4, pp. 503-533. https://doi.org/10.1007/s10458-018-9386-z

}

TY - JOUR

T1 - Coalition structure generation in cooperative games with compact representations

AU - Ueda, Suguru

AU - Iwasaki, Atsushi

AU - Conitzer, Vincent

AU - Ohta, Naoki

AU - Sakurai, Yuko

AU - Yokoo, Makoto

PY - 2018/7/1

Y1 - 2018/7/1

N2 - This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well.

AB - This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well.

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UR - http://www.scopus.com/inward/citedby.url?scp=85048631587&partnerID=8YFLogxK

U2 - 10.1007/s10458-018-9386-z

DO - 10.1007/s10458-018-9386-z

M3 - Article

AN - SCOPUS:85048631587

VL - 32

SP - 503

EP - 533

JO - Autonomous Agents and Multi-Agent Systems

JF - Autonomous Agents and Multi-Agent Systems

SN - 1387-2532

IS - 4

ER -