We study the resource allocation problem in Orthogonal Frequency Division Multiplexing (OFDM) systems as a cooperative game. The goal is to maximize the overall system rate considering fairness metrics among users. We propose Nash bargaining solution (NBS) as a tool that achieves point(s) on the Pareto frontier of the game theoretical rate region under asymmetric conditions. Moreover, we provide a practical stochastic algorithm that can converge to one of the fairness points on the Pareto boundary. The numerical results show that the NBS not only maintains fair resource allocation for all users, but also provides a desirable spectral efficiency for the OFDM system.