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We consider problems in multi-agent systems where a network of mobile sensors needs to self-organize such that some global objective function is maximized. To deal with the agents' lack of global information we approach the problem in a game-theoretic framework where agents/players are only able to access local measurements of their own local utility functions whose parameters and detailed analytical forms may be unknown. We then propose a distributed and adaptive algorithm, where each agent applies a local extremum seeking feedback adopted to its specific motion dynamics, and prove its global practical stability, implying that the agents asymptotically reach a configuration that is arbitrary close to the globally optimal one. For the stability analysis we introduce a novel methodology based on a Lie bracket trajectory approximation and combine it with a potential game approach. We apply the proposed algorithm to the sensor coverage problem and solve it in a distributed way where the agents do not need any a priori knowledge about the distribution of the events to be detected and about the detection probabilities of the individual agents. The proposed scheme is illustrated through simulations.