Distributed Learning in Secondary Spectrum Sharing Graphical Game

Secondary users sharing primary users\´ spectrum is modeled as a graphical game. Users located in random graphs and a regular lattice are considered. Secondary users are assumed to differentiate the ``quality" of the primary spectrum while interacting within their local neighborhood to minimize interference and congestion. The learning algorithm is also shown to be effective in punishing malicious users that violate spectrum etiquettes. An equivalence between spectrum sharing neighborhood interaction and the spin-glass model in statistical physics is established. A distributed exponential learning algorithm is used to arrive at an evolutionary stable solution to the game. Some theoretical properties of the system are studied and simulation results are presented to illustrate price of anarchy, convergence of the learning algorithm and asymptotic invariance of the system performance with respect to spectrum quality.