Bounded Approximate Algorithm for Probabilistic Coalition Structure Generation

How to form effective coalitions is an important issue in multi-agent systems. Coalition Structure Generation (\({\mathsf {CSG}}\)) is a fundamental problem that can formalize various applications related to multi-agent cooperation. \({\mathsf {CSG}}\) involves partitioning a set of agents into coalitions so that the social surplus (i.e. the sum of the values of all coalitions) is maximized. In the real world, it is natural to consider the uncertainty of agents’ attendances, e.g., an agent is available only two or three days a week because of his/her own schedule. In other words, there is no guarantee to establish all coalitions. Probabilistic Coalition Structure Generation (\({\mathsf {PCSG}}\)) is the extension of \({\mathsf {CSG}}\) where the attendance type of each agent is considered. The aim of this problem is to find the optimal coalition structure which maximizes the sum of the expected values of all coalitions. In \({\mathsf {PCSG}}\), since finding the optimal coalition structure becomes easily intractable, it is important to consider fast but approximate algorithms. In this paper, a formal framework for \({\mathsf {PCSG}}\) is introduced. An approximate algorithm for \({\mathsf {PCSG}}\) called Bounded Approximate Algorithm based on Attendance Types (\({\mathsf {BAAAT}}\)) is then presented. Also, we show that \({\mathsf {BAAAT}}\) can provide the theoretical bound of a solution a priori. In the experiments, \({\mathsf {BAAAT}}\) is evaluated on a number of benchmarks.