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Pay-for-priority is a common practice in congestion-prone service systems. The extant literature on this topic restricts attention to the case where the only epoch for customers to purchase priority is upon arrival, and if customers choose not to upgrade when they arrive, they cannot do so later during their wait. A natural alternative is to let customers pay and upgrade to priority at any time during their stay in the queue, even if they choose not to do so initially. This paper builds a queueing-game-theoretic model that explicitly captures self-interested customers’ dynamic in-queue priority-purchasing behavior. When all customers (who have not upgraded yet) simultaneously decide whether to upgrade, we find in our model that 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, when …