  We study strong equilibria in symmetric capacitated cost-sharing 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 variants of cost-sharing games have been previously studied: (i)
games where coalitions can form, and (ii) games where edges are associated with
capacities; both variants are inspired by real-life scenarios. In this work we
combine these variants 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 variants. Our contribution is
two-fold. 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 are qualitatively different than those obtained in the analysis of each
variant alone, and the combination of coalitions and capacities entails the
introduction of more refined topology classes than previously studied.

Computer Science and Game Theory