Sequential routing game on the line: Transmit or relay?

In this paper, we study a sequential dynamic routing game on a line where the decision of a user is spatio-temporal control. Each user ships its demand over time on a shared resource. We address the case where only one user arrives at each time epoch. The state of a player evolves according to whether he decides to transmit or not. We provide explicit expressions of the equilibrium of such systems and compare them to the global optimum case. In particular, we compute the price of anarchy of such schemes and identify a Braess-type paradox in the context of sequential routing game.