Offline Learning of Nash Stable Coalition Structures with Possibly Overlapping Coalitions

Coalition formation concerns strategic collaborations of selfish agents that form coalitions based on their preferences. It is often assumed that coalitions are disjoint and preferences are fully known, which may not hold in practice. In this paper, we thus present a new model of coalition formation with possibly overlapping coalitions under partial information, where selfish agents may be part of multiple coalitions simultaneously and their full preferences are initially unknown. Instead, information about past interactions and associated utility feedbacks is stored in a fixed offline dataset, from which we aim to efficiently infer agents' preferences. We analyze the impact of diverse dataset information constraints by studying two utility feedback models: semi-bandit (agent-level) and bandit (coalition-level) feedbacks. For both models, we identify assumptions under which the dataset covers sufficient information for an offline learning algorithm to infer preferences and use them to recover a partition that is (approximately) Nash stable, i.e., no agent can improve her utility by unilaterally deviating. We also aim to devise algorithms with low sample complexity, requiring only a small dataset to obtain a desired approximation to Nash stability. Under semi-bandit feedback, we provide a sample-efficient algorithm proven to obtain an approximately Nash stable partition under a sufficient and necessary assumption on the information covered by the dataset. Yet, under bandit feedback, we show that only a stricter assumption is sufficient for sample-efficient learning. Still, in multiple cases, our algorithms' sample complexity bounds have optimality guarantees up to logarithmic factors. Finally, extensive experiments show our algorithm's approximation to Nash stability.