Weakly-Acyclic (Internet) Routing Games

Weakly-acyclic games—a superclass of potential games—capture distributed environments where simple, globally-asynchronous interactions between strategic agents are guaranteed to converge to an equilibrium. We explore the class of routing games introduced in Fabrikant and Papadimitriou (The Complexity of Game Dynamics: BGP Oscillations, Sink Equilibria, and Beyond, pp. 844–853, 2008) and in Levin et al. (Interdomain Routing and Games, pp. 57–66, 2008), which models important aspects of routing on the Internet. We show that, in interesting contexts, such routing games are weakly acyclic and, moreover, that pure Nash equilibria in such games can be found in a computationally efficient manner.