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Consider an unobservable $M|G|1$ queue with preemptive-resume scheduling andtwo priority classes. Customers are strategic and may join the premium classfor a fee. We analyze the resulting equilibrium outcomes, equilibriumstability, and social welfare. We find that for service distributions withcoefficient of variation greater than 1, there exists a unique and stable mixedequilibrium at low loads. We also establish a tight bound on the price ofanarchy, which is $4/3$.

Social Welfare and Price of Anarchy in Preemptive Priority Queues