Strategic Behavior and No-Regret Learning in Queueing Systems

This paper studies a dynamic discrete-time queuing model where at every period players get a new job and must send all their jobs to a queue that has a limited capacity. Players have an incentive to send their jobs as late as possible; however if a job does not exit the queue by a fixed deadline, the owner of the job incurs a penalty and this job is sent back to the player and joins the queue at the next period. Therefore, stability, i.e. the boundedness of the number of jobs in the system, is not guaranteed. We show that if players are myopically strategic, then the system is stable when the penalty is high enough. Moreover, if players use a learning algorithm derived from a typical no-regret algorithm (exponential weight), then the system is stable when penalties are greater than a bound that depends on the total number of jobs in the system.