Regulation under partial cooperation: The case of a queueing system

Socially optimal behavior can be achieved through the cooperation of the participating agents with a central planner. What happens when only a fraction of the population cooperates? We investigate this question in a Markovian single server queue. The main result is non-intuitive: the optimal control of cooperative customers is independent of their proportion. We also conclude that the gain from controlling cooperative customers after they join the queue is relatively small.