Stochastic Characterization of the Spectrum Sharing Game in Ad-Hoc Communications

Resource sharing problems naturally arise in case of wireless networks where the transmission medium is inherently broadcast and transmission resources, e.g., frequency channels, transmission power levels, temporal slots, have to be orchestrated among multiple concurrent transmissions. In the paper, we consider a Gaussian Interference Game, where multiple transmitters have to decide how to split a total power budget across orthogonal spectrum bands with equal bandwidth. We provide a characterization of the game both for deterministic and random topologies. In particular, the analysis of large networks game can be simplified, by wisely decom- posing the N-player game into independent equivalent sub-games of 2-player. A heuristic algorithm is proposed to implement such decomposition, thus allowing to get the equilibria for the N-players game. Finally, a distributed algorithm is introduced to let the N players converge to equilibria conditions. Numerical simulations show that the proposed algorithm drives the users to stable points that are close to the equilibria of the game further requiring only minimal information exchange.