  This paper studies a significant problem in green networking called switching
off base stations in case of cooperating service providers by means of
stochastic geometric and coalitional game tools. The coalitional game herein
considered is played by service providers who cooperate in switching off base
stations. When they cooperate, any mobile is associated to the nearest BS of
any service provider. Given a Poisson point process deployment model of nodes
over an area and switching off base stations with some probability, it is
proved that the distribution of signal to interference plus noise ratio remains
unchanged while the transmission power is increased up to preserving the
quality of service. The coalitional game behavior of a typical player is called
to be \emph{hedonic} if the gain of any player depends solely on the members of
the coalition to which the player belongs, thus, the coalitions form as a
result of the preferences of the players over their possible coalitions' set.
We also introduce a novel concept which is called the Nash-stable core
containing those gain allocation methods that result in Nash-stable partitions.
By this way, we always guarantee Nash stability. We study the non-emptiness of
the Nash-stable core. Assuming the choice of a coalition is performed only by
one player in a point of time, we prove that the Nash-stable core is non-empty
when a player chooses its coalition in its turn, the player gains zero utility
if the chosen coalition is visited before by itself.
