This paper proposes a novel game-theoretic cross-layer design for orthogonal frequency division multiple access (OFDMA) wireless networks, which operates optimal subcarrier, power and rate allocation. Based on the Nash bargaining solution (NBS) and coalitions, the proposed scheme not only maximizes the system's effective data rate but also supports proportional fairness among the users by considering the heterogeneity of their requirements, as well as the rate outage due to imperfect channel state information (CSI) available at the transmitter (CSIT). The simulation results confirm that the proposed scheme achieves an optimum tradeoff between effective data rate and proportional fairness, while it guarantees the quality of service (QoS) requirements, and outperforms the existing solutions in terms of power consumption, resilience to CSIT errors and stability.