Do Capacity Constraints Constrain Coalitions?

TL;DR

This paper investigates the existence and efficiency of strong equilibria in symmetric capacitated cost-sharing games, revealing new phenomena and providing topological characterizations and bounds on efficiency loss.

Contribution

It combines coalition and capacity constraints in cost-sharing games, offering a topological characterization of networks with guaranteed strong equilibria and tight bounds on efficiency loss.

Findings

Characterizes networks always admitting strong equilibria.

Establishes tight bounds on the strong price of anarchy.

Reveals new phenomena due to the combination of coalitions and capacities.

Abstract

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.