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On the computation of probabilistic coalition structures
Autonomous Agents and Multi-Agent Systems ( IF 1.9 ) Pub Date : 2021-03-24 , DOI: 10.1007/s10458-021-09498-7
Nicolas Schwind , Tenda Okimoto , Katsumi Inoue , Katsutoshi Hirayama , Jean-Marie Lagniez , Pierre Marquis

In Coalition Structure Generation (CSG), one seeks to form a partition of a given set of agents into coalitions such that the sum of the values of each coalition is maximized. This paper introduces a model for Probabilistic CSG (PCSG), which extends the standard CSG model to account for the stochastic nature of the environment, i.e., when some of the agents considered at start may be finally defective. In PCSG, the goal is to maximize the expected utility of a coalition structure. We show that the problem is \({\mathsf{NP}}^{\mathsf {PP}}\)-hard in the general case, but remains in \({\mathsf{NP}}\) for two natural subclasses of PCSG instances, when the characteristic function that gives the utility of every coalition is represented using a marginal contribution network (MC-net). Two encoding schemes are presented for these subclasses and empirical results are reported, showing that computing a coalition structure with maximal expected utility can be done efficiently for PCSG instances of reasonable size. This is an extended and revised version of the paper entitled “Probabilistic Coalition Structure Generation” published in the proceedings of KR’18, pages 663–664 [33].



中文翻译:

关于概率联盟结构的计算

在联盟结构生成(CSG)中,人们试图将一组给定的代理分成一个联盟,以使每个联盟的价值之和最大化。本文介绍了概率CSG(PCSG)模型,该模型扩展了标准CSG模型以考虑环境的随机性,即,当开始时考虑的某些代理可能最终有缺陷时。在PCSG中,目标是最大化联盟结构的预期效用。我们证明问题是\({\ mathsf {NP}} ^ {\ mathsf {PP}} \)-在一般情况下很难,但仍然存在于\({\ mathsf {NP}} \\对于PCSG实例的两个自然子类,当使用边际贡献网络(MC-net)表示提供每个联盟效用的特征函数时。针对这些子类提出了两种编码方案,并报告了经验结果,表明对于合理大小的PCSG实例,可以有效地完成具有最大预期效用的联盟结构的计算。这是在KR'18会议论文集第663-664页[33]中发布的题为“概率联盟结构生成”的论文的扩展和修订版本。

更新日期:2021-03-24
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