A Price Based Decentralized Rate Selection in IEEE 802.11 Based WLANS

We consider the problem of decentralized rate selection in IEEE 802.11 wireless local area networks (WLANs). Owing to the decentralized nature of WLANs, we formulate the current problem of rate selection as a non-cooperative game where individual users (players) of a WLAN can pick their actions from a finite set of physical layer modulation rates. The utility of each user is the difference of throughput and a cost incurred due to the price imposed by the access point. We prove the resulting non-cooperative game to be supermodular, and hence has at least one pure strategy Nash equilibrium, that is contained in a set bounded by the smallest and largest Nash equilibria. We also prove the smallest and largest Nash equilibria to be non-decreasing functions of the price and the smallest Nash equilibrium to be Pareto-dominant. We present an algorithm to compute the best response of each user asynchronously, that converges almost surely to the smallest Nash equilibrium of the game. Next we extend our price based approach to the multi-channel case and prove the resulting game to be supermodular in the special case of two channels. Our simulation results demonstrate the improvement in overall network throughput with appropriate tuning of the price.