### Abstract

A Coalition Structure Generation (CSG) problem involves partitioning a set of agents into coalitions so that the social surplus is maximized. Recently, Ohta et al. developed an efficient algorithm for solving CSG assuming that a characteristic function is represented by a set of rules, such as marginal contribution networks (MC-nets). In this paper, we extend the formalization of CSG in Ohta et al. so that it can handle negative value rules. Here, we assume that a characteristic function is represented by either MC-nets (without externalities) or embedded MC-nets (with externalities). Allowing negative value rules is important since it can reduce the efforts for describing a characteristic function. In particular, in many realistic situations, it is natural to assume that a coalition has negative externalities to other coalitions. To handle negative value rules, we examine the following three algorithms: (i) a full transformation algorithm, (ii) a partial transformation algorithm, and (iii) a direct encoding algorithm. We show that the full transformation algorithm is not scalable in MC-nets (the worst-case representation size is Ω(n^{2}), where n is the number of agents), and does not seem to be tractable in embedded MC-nets (representation size would be Ω(2^{n})). In contrast, by using the partial transformation or direct encoding algorithms, an exponential blow-up never occurs even for embedded MC-nets. For embedded MC-nets, the direct encoding algorithm creates less rules than the partial transformation algorithm. Experimental evaluations show that the direct encoding algorithm is scalable, i.e., an off-the-shelf optimization package (CPLEX) can solve problem instances with 100 agents and rules within 10 seconds.

Original language | English |
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Pages | 184-191 |

Number of pages | 8 |

Publication status | Published - Jan 1 2012 |

Event | 11th International Conference on Autonomous Agents and Multiagent Systems 2012: Innovative Applications Track, AAMAS 2012 - Valencia, Spain Duration: Jun 4 2012 → Jun 8 2012 |

### Other

Other | 11th International Conference on Autonomous Agents and Multiagent Systems 2012: Innovative Applications Track, AAMAS 2012 |
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Country | Spain |

City | Valencia |

Period | 6/4/12 → 6/8/12 |

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence

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## Cite this

*Handling negative value rules in MC-net-based coalition structure generation*. 184-191. Paper presented at 11th International Conference on Autonomous Agents and Multiagent Systems 2012: Innovative Applications Track, AAMAS 2012, Valencia, Spain.