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For cooperative games with externalities, the problem of optimally partitioning a set of players into disjoint exhaustive coalitions is called  coalition structure generation , and is a fundamental computational problem in multi-agent systems. Coalition structure generation is, in general, computationally hard and a large body of work has therefore investigated the development of efficient solutions for this problem. However, the existing methods are mostly limited to deterministic environments. In this paper, we focus attention on uncertain environments. Specifically, we define  probabilistically monotone partition function games , a subclass of the well-known  partition function games  in which we introduce uncertainty. We provide a constructive proof that an exact optimum can be found using a greedy approach, present an algorithm for finding an optimum, and analyze its time complexity.

Optimal coalition structures for probabilistically monotone partition function games