Game Theoretic Cross-Layer Transmission Policies in Multipacket Reception Wireless Networks

We study the structure of the optimal transmission policies for noncooperating nodes in a finite-size random access wireless network, where the medium access control (MAC) protocol is a variant of the time-slotted ALOHA protocol. It is assumed that the network has the multipacket reception capability and every node knows its channel state information (CSI), which is continuously distributed, perfectly at the beginning of each transmission time slot. The objective of each node in the network is to find a transmission policy mapping CSI to transmission probabilities to maximize its individual utility. The problem is formulated as a noncooperative game of a finite number of rational players and actions with a continuous channel state space. We prove that if the probability of success of a node is a nondecreasing function of its CSI, there exists a threshold transmission policy that maximizes its utility. It is then shown that there exists a Nash equilibrium at which every node adopts a threshold policy. The optimality of threshold policies strongly simplifies the problem of optimizing the transmission policy for a node. We propose a stochastic-gradient-based algorithm that exhibits the best response dynamic adjustment process for the transmission game. The theoretical results of the paper as well as the performance of the proposed algorithm are illustrated via numerical examples