Strategic experimentation in queues

We analyze the social and private learning at the symmetric equilibria of a queueing game with strategic experimentation. An infinite sequence of agents arrive at a server which processes them at an unknown rate. The number of agents served at each date is either: a geometric random variable in the good state, or zero in the bad state. The queue lengthens with each new arrival and shortens if the agents are served or choose to quit the queue. Agents can only observe the evolution of the queue after they arrive; they, therefore, solve a strategic experimentation problem when deciding how long to wait to learn about the probability of service. The agents, in addition, benefit from an informational externality by observing the length of the queue and the actions of other agents. They also incur a negative payoff externality, as those at the front of the queue delay the service of those at the back. We solve for the long-run equilibrium behavior of this queue and show there are typically mass exits from the queue, even if the server is in the good state.