Equilibrium strategies and the value of information in a two line queueing system with threshold jockeying

We consider memoryless two-line system with threshold jockeying. Upon arrival each customer decides whether to purchase the information about which line is shorter, or randomly selects one of the lines. Since the decision of a customer is affected by the decision of the others, we are interested in Nash-equilibrium policies. Indeed, we show explicitly how to find these policies. We are also interested in the externalities imposed by an informed customer on the others. We derive an explicit expression for these externalities in the case that jockeying takes place as soon as the lines differ by three. Some of the results may seem to be counterintuitive. For example, when the threshold is three, the value of information may increase with the portion of informed customers.