Routing game on the line: The case of multi-players

In this paper, we study a sequential routing game networks where M users send traffic to a destination on a line. Each user arrives at time epoch with a given capacity. Then, he ships its demand over time on a shared resource. The state of a player evolves according to whether he decides to transmit or not. The decision of each user is thus spatio-temporal control. We provide explicit expression of the equilibrium of such systems and compare it to the global optimum case. In particular, we compute the price of anarchy of such scheme and identify a Braess-type paradox in the context of sequential routing game.