Dynamic Pricing and Queue Stability in Wireless Random Access Games

We study the interaction among users of contention-based wireless networks, where the performance of the network is highly correlated with user transmission probabilities. Considering the underlying user incentives, we make use of the conceptual framework of noncooperative game theory to obtain a distributed control mechanism to limit the contention among wireless nodes by taking into account queue stability and injecting linear pricing to punish greedy behavior. We present a comprehensive analysis of the game including existence and uniqueness of Nash equilibrium point, convergence dynamics, and robustness properties. Utilizing linear pricing enables us to move the equilibrium point of the game to a desirable region. We obtain conditions on linear prices necessary to achieve stability of user queues in the asymmetric and symmetric cases. In addition, we propose dynamic pricing algorithms, in which wireless users play the game without cooperation while the base station adjusts the linear price of each user. Under limited knowledge of game parameters, we present a dynamic equal pricing algorithm that moves the Nash equilibrium to the aggregate throughput maximizing solution. The theoretical results are verified, and the convergence and efficiency of the proposed game are illustrated via simulations.