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In many practical scenarios, wireless mesh clients are autonomous and thus, may exhibit non-cooperative behaviors due to self-interests. For instance, a client may report bogus channel information to a mesh router in order to gain resource allocation advantages. Such non-cooperative behaviors are practicable as the client device's software could be modified by the user. In this paper, we analyze the impact of these rationally selfish and non-cooperative behaviors on the performance of packet scheduling algorithms in wireless mesh networks. Using a mixed strategy game theoretic model, we found that the traditional rate maximizing packet scheduling algorithms can lead non-cooperative clients to an undesirable Nash equilibrium, in which the wireless channel is used inefficiently. Motivated by this observation, we propose a novel repeated game theoretic approach to optimize packet scheduling and achieve efficient equilibria.