Non-Cooperative Transmission Game in Wireless Networks with Multipacket Reception and Packet Priority

We consider the uplink of random access multipacket reception wireless sensor networks where packets may have different priorities. Each sensor aims to optimize its transmission policy, which maps instantaneous channel states and packet priorities to transmit probabilities, to maximize its individual reward. The problem is formulated as a non-cooperative game. We show that the optimal transmission policies have a special structure: given a packet priority, it is optimal for a sensor to transmit with certainty if its channel state is beyond a certain threshold and not to transmit otherwise. We prove that there exists a Nash equilibrium profile at which every sensor deploys a transmission policy of this structure. A convergent stochastic approximation algorithm is proposed for estimating the best response transmission policy for any sensor. The theoretical results and the performance of the proposed algorithm are illustrated via numerical examples.