  We consider a set of cellular users associated with a base station (BS) in a
cellular network that employs Device-to-device (D2D) communication. A subset of
the users request for some files from the BS. Now, some of the users can
potentially act as relays and forward the requested files, or partitions of
files, from the BS to some of the requesting users (destination nodes) over D2D
links. However, this requires cooperation among the cellular users. In this
paper, we seek conditions under which users have an incentive to cooperate with
each other. We model the above scenario using the frameworks of cooperative
game theory and stable partitions in coalitional games. We consider two
different models for file transfer within a coalition: (i) Model A, in which
the BS can split a file into multiple partitions and send these partitions to
different relays, which multicast the partitions to the destination nodes of
the coalition, and (ii) Model B, in which for each file, the BS sends the
entire file to a single relay, which multicasts it to the destination nodes of
the coalition. First, we explore the question of whether it is beneficial for
all the cellular users to cooperate, i.e., whether the grand coalition is
stable. For this we use the solution concept of core from cooperative game
theory. We show that, in general, the above coalitional game under Model A may
have an empty core. Next, we provide conditions under which the core is always
non-empty and a D_c-stable partition always exists. Also, we show that under
Model B, the problem of assigning relays to destination nodes so as to maximize
the sum of utilities of all the users is NP-Complete. Finally, we show via
numerical computations that a significant reduction in the energy expenditure
of cellular users can be achieved via cooperation.
