Equilibrium behavior under non-FCFS priority rules with optimal information

Characterize the equilibrium entry and abandonment strategies of buyers in the NTU M/M/1 model under non-FCFS queueing disciplines—specifically Service-In-Random-Order (SIRO), Load-Independent Expected Waiting (LIEW), Last-Come-First-Served (LCFS), and LCFS with preemption—when the optimal information policy is used and the recommendation to join up to two and then stay until served cannot be sustained; determine whether and how mixed abandonment or excessive entry emerges in equilibrium.

Background

The authors compare residual mean wait times across several priority rules under an optimal information policy. FCFS yields decreasing residual waits, sustaining the recommendation to stay until service. By contrast, SIRO, LIEW, LCFS, and LCFS-PR lead to increasing residual waits, undermining the recommendation to stay.

They note that under these alternative disciplines, the standard equilibrium in which buyers join (up to a cap) and remain is not viable. While they speculate that randomization in abandonment or excessive entry might occur, they explicitly state that the equilibrium outcome is unclear and leave characterization open.

References

The figure implies that under each of the other queueing rules, it cannot be an equilibrium that agents will join the queue up to two and stay until they are served. It is unclear what will happen in equilibrium; they may randomize in leaving the queue, and/or they may excessively enter with a plan to leave soon after.

— Dynamic Market Design  (2601.00155 - Che, 1 Jan 2026) in Section "Information Design and the Optimality of FCFS" (discussion around Figure "Expected wait times under alternative queueing rules")