In-Queue Priority Purchase : A Dynamic Game Approach

Pay-for-priority is a common practice in congestion-prone service systems. In many applications, customers are allowed to pay and upgrade to priority at any time of their stay in the queue, even if they choose not to do so initially. However, this dynamic in-queue priority-purchasing behavior of strategic customers has been unexplored in the extant literature, which, instead, assumes that the only epoch to purchase priority is upon arrival, and if customers choose not to upgrade, they cannot do so later during their wait. To fill this gap, we build a queueing-game-theoretic model in this paper that explicitly captures customers' in-queue priority-purchasing behavior. We show that under the assumption that all customers (who have not upgraded yet) simultaneously decide whether to upgrade, pure-strategy equilibria do not exist under some intuitive criteria, contrasting the findings in classical models where customers can only purchase priority upon arrival. However, under the sequential upgrade rule, pure-strategy equilibria may exist, which we confirm analytically in a small buffer system and in a general buffer system with sufficiently light or heavy traffic, and numerically in a system that can hold at most three customers. Regardless of the rule in use, in-queue priority purchase yields less revenue than upon-arrival priority purchase in a small buffer system