This paper explores Martingale processes in a fair game scenario where secondary users attempt to efficiently access the frequency spectrum resources in a time division multiple access (TDMA) wireless network. Through the leveraging of Martingale characteristics, the secondary users have the ability to evolve holistically; thus, making better decisions about the system state over time. Simulation results show that the proposed approach is more robust and reliable in non-convex cases than other methods which rely on multiple parameters that must be fine-tuned. It also demonstrates that the secondary users can efficiently collaborate on accessibility within each opportunistic window frame of time.