Timed Congestion Games with Application to Multi-Fleet Platoon Matching

This paper introduces the notion of timed congestion games with agent-specific benefit functions to solve the problem of multi-route multi-fleet platoon matching. The fact that the timed congestion game with agent-specific benefit functions is isomorphic to the congestion game with agent-specific benefit functions is shown. Furthermore, two subclasses of the timed congestion game with agent-specific benefit functions are shown to possess a Nash equilibrium. In addition, in both subclasses, every best response sequence is proven to have finite length. Then, the theoretical results on the timed congestion game with agent-specific benefit functions are applied to the problem of multi-route multi-fleet platoon matching. We illustrate our approach with a numerical example.