## Coalition Structure Generation with Worst Case Guarantees (1999)

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Citations: | 209 - 10 self |

### BibTeX

@MISC{Sandholm99coalitionstructure,

author = {Tuomas Sandholm and Kate Larson and Martin Andersson and Onn Shehory and Fernando Tohmé},

title = {Coalition Structure Generation with Worst Case Guarantees},

year = {1999}

}

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### Abstract

Coalition formation is a key topic in multiagent systems. One may 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 exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NP-complete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also significantly outperforms its obvious contenders. Finally, we show how to distribute the desired

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Citation Context ...re generation activity is resource-bounded: not all coalition structures can be enumerated. Our model of coalition structure generation Let A be the set of agents, and a = jAj. As is common practice (=-=Kahan & Rapoport 1984-=-; Shehory & Kraus 1995; 1996; Zlotkin & Rosenschein 1994; Ketchpel 1994; Sandholm & Lesser 1997), we study coalition formation in characteristic function games (CFGs). In such games, the value of each... |

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Citation Context ...lgorithms and on-line search control policies for coalition structure generation. We are also analyzing the interplay of dynamic coalition formation and belief revision among bounded-rational agents (=-=Tohme & Sandholm 1997-=-). The long term goal is to construct normative methods that reduce the complexity|in the number of agents and in the size of each coalition's optimization problem|for coalition structure generation, ... |

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Citation Context ...s and on-line search control policies for coalition structure generation. We are also analyzing the interplay of dynamic coalition formation and belief revision among bounded-rational agents (Tohme & =-=Sandholm 1997-=-). The long term goal is to construct normative methods that reduce the complexity|in the number of agents and in the size of each coalition's optimization problem|for coalition structure generation, ... |

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Citation Context ... without trying at least 2a,1 coalition structures. This sheds light on earlier algorithms. Speci cally, all prior coalition structure generation algorithms for general characteristic function games (=-=Shehory & Kraus 1996-=-; Ketchpel 1994)|which we know of|fail to establish such a bound. In other words, the coalition structure that they nd may be arbitrarily far from optimal. Lowering the bound with further search We ha... |

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