Mobile social networks and location-aware applications are becoming more and more widespread in current wireless networks. Thanks to WiFi or Bluetooth-enabled devices, everyday mobile users can enjoy new services. However, the deployment of these mobile technologies leads to many concerns for privacy, especially location privacy. In wireless networks, external malicious parties can monitor pseudonyms used for identification to learn mobile users' location and track their movements. A common technique for protecting location privacy consists in changing pseudonyms in regions called mix zones. In this report, we present a game-theoretic approach to evaluate the interaction and behaviors of an attacker aiming to jeopardize mobile nodes' location privacy and nodes willing to thwart adversary's spiteful plans. Assuming that such an attacker is armed with local eavesdropping devices, he must deploy them in an efficient way to track as many nodes as possible. On the other hand, mobile users have to define where are the best places to locate their mix zones. In order to evaluate their potential benefit, mobile nodes need to know the mixing effectiveness of possible mix zone locations. We propose a simplified metric based on the mobility profiles to determine the location privacy achieved with mix zones. We also build a payoff model to deal with costs, as well as benefits, led by this extended hide-and-seek game. By means of analytical and numerical results, we show the existence of Nash equilibria for all values of players' costs and mobility parameters. We prove that the adversary's best behavior evolves regarding the benefit he gets from traffic sniffing and the cost led by deployment of eavesdropping stations. On the other hand, we show that, when the mobility profile is homogeneous, the mobile nodes' best response is independent of the adversary's deployment of sniffing stations. Furthermore, the nodes' best response is only dependent on the number of mix zones they deploy, not on their particular locations.
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