A Bayesian Overlapping Coalition Formation Game for Device-to-Device Spectrum Sharing in Cellular Networks

We consider the spectrum sharing problem between a set of device-to-device (D2D) links and multiple co-located cellular networks. Each cellular network is controlled by an operator which can provide service to a number of subscribers. Each D2D link can either access a sub-band occupied by a cellular subscriber or obtain an empty sub-band for its exclusive use. We introduce a new spectrum sharing mode for D2D communications in cellular networks by allowing two or more D2D links with exclusive use of sub-bands to share their sub-bands with each other without consulting the operators. We establish a new game theoretic model called Bayesian non-transferable utility overlapping coalition formation (BOCF) game. We show that our proposed game can be used to model and analyze the above spectrum sharing problem. However, we observe that the core of the BOCF game can be empty, and we derive a sufficient condition for which the core is non-empty. We propose a hierarchical matching algorithm which can detect whether the sufficient condition is satisfied and, if it is satisfied, achieve a stable and unique matching structure which coincides with the overlapping coalition agreement profile in the core of the BOCF game.