The curse of the first-in-first-out queue discipline

We consider a game in which a large number of identical agents choose when to queue up at a single server after it opens. Agents are impatient for service and also incur a cost proportional to time spent in the queue. We show that the first-in-first-out queue discipline and the last-in-first-out queue discipline both lead to a unique equilibrium arrival distribution. However, among all work-conserving queue disciplines, the first-in-first-out performs the worst in terms of equilibrium utility and welfare, while the last-in-first-out performs the best.