Spectrum Sharing Between Wireless Networks

We consider the problem of two wireless networks operating on the same (presumably unlicensed) frequency band. Pairs within a given network cooperate with one another, but between networks there is competition for spectrum. To make the problem tractable, we assume transmissions are scheduled according to a random access protocol where each network chooses an access probability for its users. In this vein a game between the two networks is defined. We characterize the Nash Equilibrium behavior of the system. Three regimes are identified; a full-spread regime, where both networks choose to simultaneously schedule all transmissions; a partial-spread regime, where one network schedules all transmissions and the other only schedules a fraction; and a joint-spread regime, where both networks schedule a fraction of their transmissions. The regime of operation depends on the pathloss exponent alpha. The joint-spread regime, which has a cooperative flavor, is attainable only for alpha > 4, which suggests that in certain environments there may be a natural incentive for rival wireless networks to cooperate.