In mobile networks, authentication is a required primitive for most security protocols. Unfortunately, an adversary can monitor pseudonyms used for authentication to track the location of mobile nodes. A frequently proposed solution to protect location privacy suggests that mobile nodes collectively change their pseudonyms in regions called mix zones. This approach is costly. Self-interested mobile nodes might, thus, decide not to cooperate and jeopardize the achievable location privacy. In this paper, we analyze non-cooperative behavior of mobile nodes by using a game-theoretic model, where each player aims at maximizing its location privacy at a minimum cost. We obtain Nash equilibria in static n-player complete information games. As in practice mobile nodes do not know their opponents' payoffs, we then consider static incomplete information games. We establish that symmetric Bayesian-Nash equilibria exist with simple threshold strategies. By means of numerical results, we predict behavior of selfish mobile nodes. We then investigate dynamic games where players decide to change their pseudonym one after the other and show how this affects strategies at equilibrium. Finally, we design protocols-PseudoGame protocols-based on the results of our analysis and simulate their performance in vehicular network scenarios.