Strategic Open Routing in Service Networks

We study the behavior of strategic customers in an open-routing service network with multiple stations. When a customer enters the network, she is free to choose the sequence of stations that she visits, with the objective of minimizing her expected total system time. We propose a two-station game with all customers present at the start of service and deterministic service times, and we find that strategic customers “herd,” i.e., in equilibrium all customers choose the same route. For unobservable systems, we prove that the game is supermodular, and we then identify a broad class of learning rules—which includes both fictitious play and Cournot best-response—that converges to herding in finite time. By combining different theoretical and numerical analyses, we find that the herding behavior is prevalent in many other congested open-routing service networks, including those with arrivals over time, those with stochastic service times, and those with more than two stations. We also find that the system under herding performs very close to the first-best outcome in terms of cumulative system time.