Spatio-temporal Control for Dynamic Routing Games

In this paper, we study dynamic routing games where the decision of an user is spatio-temporal control. Each user ships its demand over time on a shared resource. We investigate the equilibrium of such systems and show the existence and uniqueness of equilibrium. In the second part, we study a stochastic congestion games where there is only one shared resource and the traffic is indivisible. The information structure that we consider is such that each user knows the state of its own buffer but not aware of states and the actions taken by other users. The game can be described as a game with random environment. We manage to characterize the structure of equilibria policies using linear programming.