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We analyze a static pricing scheme for priority services. Users are free to choose the priority of their traffic but are charged accordingly. Using a game theoretic framework, we study the case where users choose priorities to maximize their net benefit. For the single link case, we show that there always exists an equilibrium for the corresponding game; however, the equilibrium is not necessarily unique. Furthermore, we show that packet loss in equilibrium can be expressed as a function of the prices associated with the different priority classes. We provide a numerical case study to illustrate our results.