Routing (Un-) Splittable Flow in Games with Player-Specific Linear Latency Functions

In this work we study weighted network congestion games with playerspecific latency functions where selfish players wish to route their traffic through a shared network. We consider both the case of splittable and unsplittable traffic. Our main findings are as follows: – For routing games on parallel links with linear latency functions without a constant term we introduce two new potential functions for unsplittable and for splittable traffic respectively. We use these functions to derive results on the convergence to pure Nash equilibria and the computation of equilibria. We also show for several generalizations of these routing games that such potential functions do not exist. – We prove upper and lower bounds on the price of anarchy for games with linear latency functions. For the case of unsplittable traffic the upper and lower bound are asymptotically tight.