Nowadays most mobile devices are equipped with multiple network interfaces such as cellular network interface, Wi-Fi interface, and Ethernet. An access network selection mechanism is required during the transmission phrase to provide the best performance and resource utilization. In this paper, we model the access network selection problem as a repeated stochastic game with consideration of optical networks, terrestrial wireless networks, airborne networks and satellite networks. With the goals of maximizing total user utility and achieving maximum proportional fairness, the access network selection problem is solved using the Lyapunov optimization algorithm. Simulation results demonstrate that the proposed repeated stochastic game approach achieves higher total utility and larger proportional fairness index, compared to two benchmark schemes.