Channel allocation is a crucial concern in variable-width wireless local area networks. This work aims to obtain the stable and fair nonoverlapped variable-width channel allocation for selfish access points (APs). In the scenario of single collision domain, the channel allocation problem reduces to a channel-width allocation problem, which can be formulated as a noncooperative game. The Nash equilibrium (NE) of the game corresponds to a desired channel-width allocation. A distributed algorithm is developed to achieve the NE channel-width allocation that globally maximizes the network utility. A punishment-based cooperation self-enforcement mechanism is further proposed to ensure that the APs obey the proposed scheme. In the scenario of multiple collision domains, the channel allocation problem is formulated as a constrained game. Penalty functions are introduced to relax the constraints and the game is converted into a generalized ordinal potential game. Based on the best response and randomized escape, a distributed iterative algorithm is designed to achieve a desired NE channel allocation. Finally, computer simulations are conducted to validate the effectiveness and practicality of the proposed schemes.