  The business potential of device-to-device (D2D) communication including
public safety and vehicular communications will be realized only if direct
communication between devices subscribed to different mobile operators (OPs) is
supported. One possible way to implement inter-operator D2D communication may
use the licensed spectrum of the OPs, i.e., OPs agree to share spectrum in a
co-primary manner, and inter-operator D2D communication is allocated over
spectral resources contributed from both parties. In this paper, we consider a
spectrum sharing scenario where a number of OPs construct a spectrum pool
dedicated to support inter-operator D2D communication. OPs negotiate in the
form of a non-cooperative game about how much spectrum each OP contributes to
the spectrum pool. OPs submit proposals to each other in parallel until a
consensus is reached. When every OP has a concave utility function on the
box-constrained region, we identify the conditions guaranteeing the existence
of a unique equilibrium point. We show that the iterative algorithm based on
the OP's best response might not converge to the equilibrium point due to
myopically overreacting to the response of the other OPs, while the Jacobi-play
strategy update algorithm can converge with an appropriate selection of update
parameter. Using the Jacobi-play update algorithm, we illustrate that
asymmetric OPs contribute an unequal amount of resources to the spectrum pool;
However all participating OPs may experience significant performance gains
compared to the scheme without spectrum sharing.
