On Singleton Congestion Games with Resilience Against Collusion

TL;DR

This paper introduces a new method to prove the existence of resilient equilibrium outcomes in singleton congestion games, ensuring stability against various coalition deviations, which is a significant advancement in the field.

Contribution

It provides the strongest known existence guarantees for equilibrium outcomes resilient to weakly improving deviations by coalitions in singleton congestion games.

Findings

Existence of Nash equilibria resilient to singletons.

Existence of Pareto efficient outcomes resilient to grand coalition deviations.

Existence of partition equilibria resilient to coalition deviations.

Abstract

We study the subclass of singleton congestion games with identical and increasing cost functions, i.e., each agent tries to utilize from the least crowded resource in her accessible subset of resources. Our main contribution is a novel approach for proving the existence of equilibrium outcomes that are resilient to weakly improving deviations: $(i)$ by singletons (Nash equilibria), $(ii)$ by the grand coalition (Pareto efficiency), and $(iii)$ by coalitions with respect to an a priori given partition coalition structure (partition equilibria). To the best of our knowledge, this is the strongest existence guarantee in the literature of congestion games that is resilient to weakly improving deviations by coalitions.