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Users of mobile networks can change their identifiers in regions called mix zones in order to defeat the attempt of third parties to track their location. Mix zones must be deployed carefully in the network to reduce the cost they induce on mobile users and to provide high location privacy. Unlike most previous works that assume a global adversary, we consider a local adversary equipped with multiple eavesdropping stations. We study the interaction between the local adversary deploying eavesdropping stations to track mobile users and mobile users deploying mix zones to protect their location privacy. We use a game-theoretic model to predict the strategies of both players. We derive the strategies at equilibrium in complete and incomplete information scenarios and propose an algorithm to compute the equilibrium in a large network. Finally, based on real road-traffic information, we numerically quantify the effect of complete and incomplete information on the strategy selection of mobile users and of the adversary. Our results enable system designers to predict the best response of mobile users with respect to a local adversary strategy, and thus to select the best deployment of countermeasures.