  We consider a network composed of two interfering point-to-point links where
the two transmitters can exploit one common relay node to improve their
individual transmission rate. Communications are assumed to be multi-band and
transmitters are assumed to selfishly allocate their resources to optimize
their individual transmission rate. The main objective of this paper is to show
that this conflicting situation (modeled by a non-cooperative game) has some
stable outcomes, namely Nash equilibria. This result is proved for three
different types of relaying protocols: decode-and-forward,
estimate-and-forward, and amplify-and-forward. We provide additional results on
the problems of uniqueness, efficiency of the equilibrium, and convergence of a
best-response based dynamics to the equilibrium. These issues are analyzed in a
special case of the amplify-and-forward protocol and illustrated by simulations
in general.
