Computing Stable Solutions in Threshold Network Flow Games With Bounded Treewidth

Aldo Pacchiano, Yoram Bachrach

Abstract: Network flow games are a prominent model for team formation, where a commodity can flow through a network whose edges are controlled by selfish agents. In Threshold Network Flow Games (TNFGs), an agent team is successful if the flow it can achieve between a source and target vertices meets or exceeds a certain threshold. Cooperative game theory allows predicting how agents are likely to share the the joint reward in such settings, by applying solution concepts such as the core, which characterizes stable reward distributions. When TNFGs have empty cores, every reward distribution is somewhat unstable, which requires using a relaxed solution such as the least-core to find the most stable distribution. Earlier work showed that computing the least-core in TNFGs is computationally hard, but tractable for very restricted graphs, such as layer graphs. We extend these results, presenting polynomial algorithms for the much larger class of bounded-treewidth graphs.