Do Capacity Constraints Constrain Coalitions?

Abstract

We study strong equilibria in symmetric capacitated cost-sharing connection games. In these games, a graph with designated source s and sink t is given, and each edge is associated with some cost. Each agent chooses strategically an s - t path, knowing that the cost of each edge is shared equally between all agents using it. Two settings of cost-sharing connection games have been previously studied: (i) games where coalitions can form, and (ii) games where edges are associated with capacities ; both settings are inspired by real-life scenarios. In this work we combine these scenarios and analyze strong equilibria (profiles where no coalition can deviate) in capacitated games. This combination gives rise to new phenomena that do not occur in the previous settings. Our contribution is twofold. First, we provide a topological characterization of networks that always admit a strong equilibrium. Second, we establish tight bounds on the efficiency loss that may be incurred due to strategic behavior, as quantified by the strong price of anarchy (and stability) measures. Interestingly, our results qualitatively differ from those obtained in the analysis of each scenario alone, and the combination of coalitions and capacities entails the introduction of more refined topology classes than previously studied.