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. For the two-station game with deterministic service times, we prove that the game is supermodular. By applying the supermodularity result, we observe that strategic customers "herd," i.e., in equilibrium all customers choose the same route. 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.  We also find that the herding behavior is prevalent in many other open-routing service networks, including those with stochastic service times and those with more than two stations.