  Consider a wireless broadcast device-to-device (D2D) network wherein users'
devices are interested in receiving some popular files. Each user's device
possesses part of the content which is acquired in previous transmissions and
cooperates with others to recover the missing packets by exchanging Instantly
Decodable Network Coding (IDNC) packets. Recently, a distributed solution,
relying on a non-cooperative game-theoretic formulation, has been proposed to
reduce the communication time for fully connected D2D networks, i.e.,
single-hop D2D networks. In this paper, we develop a distributed
game-theoretical solution to reduce the communication time for a more realistic
scenario of a decentralized and partially connected, i.e., multi-hop,
IDNC-enabled D2D network. The problem is modeled as a coalition game with
cooperative-players wherein the payoff function is derived so that decreasing
individual payoff results in the desired cooperative behavior. Given the
intractability of the formulation, the coalition game is relaxed to a coalition
formation game (CFG) involving the formation of disjoint coalitions. A
distributed algorithm relying on merge-and-split rules is designed for solving
the relaxed problem. The effectiveness of the proposed solution is validated
through extensive numerical comparisons against existing methods in the
literature.
