This paper proposes a game-theoretic random channel access model, compliant with the IEEE 802.11 standard that can be integrated into the distributed coordination function. The objective is to design a game theoretic model that can optimize both throughput and channel access delay in each node in the presence of hidden terminals and thus optimize fairness. We propose a utility function that can decouple the protocol's dynamic adaptation to channel load from collision detection. We demonstrate that our model can reach a Nash equilibrium resulting in a stable contention window, provided that a node adapts its behavior to the idle rate of the broadcast channel, coupled with observation of its own transmission activity. Simulation results show that this model is capable of achieving lower channel access delay and better throughput than the standard IEEE 802.11 distributed coordination function.