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Channel assignment is a very important topic in wireless networks. In this paper, we study FDMA channel assignment in a noncooperative wireless network, where devices are selfish. Existing work on this problem has considered Nash Equilibrium (NE), which is not a very strong solution concept and may not guarantee a good system performance. In contrast, in this work, we introduce a payment formula to ensure the existence of a Strongly Dominant Strategy Equilibrium (SDSE), a different solution concept that gives participants much stronger incentives. We show that, when the system converges to an SDSE, it also achieves global optimality in terms of system throughput. Furthermore, we extend our work to the case in which some radios have a limited tunability. We show that in such a case, nevertheless, it is generally impossible to have a similar SDSE solution; with additional assumptions on the numbers of radios and the types of channels, etc., we can again achieve an SDSE solution that guarantees optimal system throughput. Besides this extension, we also consider other extensions of our strategic game to achieve throughput fairness and to deal with possibly inconsistent information caused by players joining and leaving. Finally, we evaluate our design with simulated experiments. Numerical results verify that the system does converge to the globally optimal channel assignment with the proposed payment formula, and that the system throughput is significantly higher than that achievable with the random-based and NE-based channel assignment schemes.