## Anytime Coalition Structure Generation: An Average Case Study (2000)

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Venue: | Journal of Experimental and Theoretical AI |

Citations: | 32 - 4 self |

### BibTeX

@ARTICLE{Larson00anytimecoalition,

author = {Kate S. Larson and Tuomas W. Sandholm},

title = {Anytime Coalition Structure Generation: An Average Case Study},

journal = {Journal of Experimental and Theoretical AI},

year = {2000},

volume = {12},

pages = {40--47}

}

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### Abstract

Abstract. Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow for exhaustive search for the optimal one. We present experimental results for three anytime algorithms that search the space of coalition structures. We show that, in the average case, all three algorithms do much better than the recently established theoretical worst case results in Sandholm et al. (1999a). We also show that no one algorithm is dominant. Each algorithm’s performance is in¯uenced by the particular instance distribution, with each algorithm outperforming the others for diŒerent instances. We present a possible explanation for the behaviour of the algorithms and support our hypothesis with data collected from a controlled experimental run. K eywords: coalition structure, algorithm, multiagent systems 1.

### Citations

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Citation Context ...general CFGs. Coalitional bargaining addresses both coalition formation and payoŒ distribution. Coalitional bargaining is seen as a generalization of the Rubinstein alternating oŒer bargaining model (=-=Rubinstein 1982-=-). A typical model has agents sequentially making proposals to the group. A proposal consists of a possible coalition to be formed and a payoŒ vector determining how the value of the coalition would b... |

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408 |
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Citation Context ... agents, and a = jAj. As is common practice (Sandholm and Lesser 1997, Shehory and Kraus 1996, Ketchpel 1994, Zlotkin and Rosenschein 1994, Kahan and Rapoport 1984, RaiŒa 1982, Wu 1977, Stearns 1968, =-=Shapley 1953-=- ) we study coalition formation in characteristic function games (CFGs). In such games, the value of each coalition S is given by a characteristic function vS. (These coalition values vS may represent... |

313 | Computationally manageable combinatorial auctions
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Citation Context ...own, instead of only knowing the coalition structure values. In these situations, coalition structure generation becomes very similar to winner determination in combinatorial auctions (Sandholm 1999, =-=Rothkopf et al. 1998-=- ). We are interested in seeing how our results apply to this new domain, and whether we can use results from combinatorial auctions for coalition structure generation. We are also analysing the inter... |

271 | Methods for task allocation via agent coalition formation
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(Show Context)
Citation Context ...nly handle one task eachÐand allocates tasks to the coalitions. Recently Shehory and Kraus have extended this work to overlapping coalitions and coalitions that can jointly handle more than one task (=-=Shehory and Kraus 1998-=-). The complexity of the problem is reduced by limiting the number of agents per coalition. The greedy algorithm guarantees that the solution is within a loose ratio bound from the best solution that ... |

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202 |
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Citation Context ...factors are insigni®cant. a xisAnytime coalition structure generation 37 7. Related research Coalition formation has been widely studied in game theory (Bernheim et al. 1987, Kahan and Rapoport 1984, =-=Aumann 1959-=-). They mainly address the question of how to divide V (CS * ) among agents so as to achieve stability of the payoŒ con®guration. However, most of that work has not taken into account the computationa... |

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Citation Context ...e indeed explain the observed behaviour: other factors are insigni®cant. a xisAnytime coalition structure generation 37 7. Related research Coalition formation has been widely studied in game theory (=-=Bernheim et al. 1987-=-, Kahan and Rapoport 1984, Aumann 1959). They mainly address the question of how to divide V (CS * ) among agents so as to achieve stability of the payoŒ con®guration. However, most of that work has n... |

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54 |
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Citation Context ...ration in characteristic function gam es Let A be the set of agents, and a = jAj. As is common practice (Sandholm and Lesser 1997, Shehory and Kraus 1996, Ketchpel 1994, Zlotkin and Rosenschein 1994, =-=Kahan and Rapoport 1984-=-, RaiŒa 1982, Wu 1977, Stearns 1968, Shapley 1953 ) we study coalition formation in characteristic function games (CFGs). In such games, the value of each coalition S is given by a characteristic func... |

47 | A Noncooperative Coalitional Bargaining Game with Random Proposers - Okada - 1996 |

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14 |
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Citation Context ... es Let A be the set of agents, and a = jAj. As is common practice (Sandholm and Lesser 1997, Shehory and Kraus 1996, Ketchpel 1994, Zlotkin and Rosenschein 1994, Kahan and Rapoport 1984, RaiŒa 1982, =-=Wu 1977-=-, Stearns 1968, Shapley 1953 ) we study coalition formation in characteristic function games (CFGs). In such games, the value of each coalition S is given by a characteristic function vS. (These coali... |

12 | Coalitional bargaining with competition to make offers - Evans - 1997 |

8 |
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Citation Context ... is N P -complete (Sandholm et al. 1999a ). 2.2. Lack of prior attention Coalition structure generation has not received much attention previously. Research has focused (Zlotkin and Rosenschein 1994, =-=Lundgren et al. 1992-=-, Van der Linden and Verbeek 1985, Kahan and Rapoport 1984, RaiŒa 1982 ) on superadditive games, i.e. gam es where v SÄT &vS + vT for all disjoint coalitions S, T Í A. In such games, coalition structu... |

4 |
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Citation Context ...e computational limitations involved. This section reviews some of the work that has been done on the computational aspects. Early work in the ®eld includes Friend’s program (Kahan and Rapoport 1984, =-=Friend 1973-=-) that simulates a 3-agent coalition formation situation where agents can make oŒers, acceptances, and rejections to each other regarding coalitions and payoŒ s. In the model, at most one oŒer regardi... |

4 | Sandholm: Negotiation Among Self-Interested Computationally Limited Agents - W - 1996 |

2 | The Nakamura theorem for coalition structures of quota games - Deb, Weber, et al. - 1996 |

1 | A noncoope rative theory of coalitional bargaining - unknown authors - 1993 |

1 |
The Art and Science of Negotiation (Cambridge MA
- RaiŒa
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(Show Context)
Citation Context ...function gam es Let A be the set of agents, and a = jAj. As is common practice (Sandholm and Lesser 1997, Shehory and Kraus 1996, Ketchpel 1994, Zlotkin and Rosenschein 1994, Kahan and Rapoport 1984, =-=RaiŒa 1982-=-, Wu 1977, Stearns 1968, Shapley 1953 ) we study coalition formation in characteristic function games (CFGs). In such games, the value of each coalition S is given by a characteristic function vS. (Th... |

1 | An algorithm for optimal winner determinism in combinatorial auctions - W - 1999 |

1 | Advantages of a leveled commitm ent contracting protocol - W, Lesser - 1996 |

1 |
Algorithms for optimizing leveled commitm ent contracts
- Sandholm, Sikka, et al.
- 1999
(Show Context)
Citation Context ...oblem includes only the coalitions with strictly positive value, no algorithm can ®nd the optimal coalition structure in polynomial time in the size of the input because the problem is N P -complete (=-=Sandholm et al. 1999-=-a ). 2.2. Lack of prior attention Coalition structure generation has not received much attention previously. Research has focused (Zlotkin and Rosenschein 1994, Lundgren et al. 1992, Van der Linden an... |

1 | Revenue equivalence of leveled commitm ent contracts - T, Zhou - 1999 |

1 |
A kernel-oriented model for coalition form ation in general environm ents: Implementation and Results
- Shehory, Kraus
- 1996
(Show Context)
Citation Context ...earch and directions for future research. 2. Coalition structure generation in characteristic function gam es Let A be the set of agents, and a = jAj. As is common practice (Sandholm and Lesser 1997, =-=Shehory and Kraus 1996-=-, Ketchpel 1994, Zlotkin and Rosenschein 1994, Kahan and Rapoport 1984, RaiŒa 1982, Wu 1977, Stearns 1968, Shapley 1953 ) we study coalition formation in characteristic function games (CFGs). In such ... |

1 |
Converg ent transfer schemes for n-person games
- Stearns
- 1968
(Show Context)
Citation Context ... be the set of agents, and a = jAj. As is common practice (Sandholm and Lesser 1997, Shehory and Kraus 1996, Ketchpel 1994, Zlotkin and Rosenschein 1994, Kahan and Rapoport 1984, RaiŒa 1982, Wu 1977, =-=Stearns 1968-=-, Shapley 1953 ) we study coalition formation in characteristic function games (CFGs). In such games, the value of each coalition S is given by a characteristic function vS. (These coalition values vS... |

1 | Coalition form ation: A game theoretic approach - Linden, Verbeek - 1985 |