  We study multi-hop data-dissemination in a wireless network from one source
to multiple nodes where some of the nodes of the network act as re-transmitting
nodes and help the source in data dissemination. In this network, we study two
scenarios; i) the transmitting nodes do not need an incentive for transmission
and ii) they do need an incentive and are paid by their corresponding receiving
nodes by virtual tokens. We investigate two problems; P1) network power
minimization for the first scenario and P2) social cost minimization for the
second scenario, defined as the total cost paid by the nodes of the network for
receiving data. In this paper, to address P1 and P2, we propose centralized and
decentralized approaches that determine which of the nodes of the network
should act as transmitting nodes, find their transmit powers and their
corresponding receiving nodes. For the sake of energy efficiency, in our model,
we employ maximal-ratio combining (MRC) at the receivers so that a receiver can
be served by multiple transmitters. The proposed decentralized approach is
based on a non-cooperative cost-sharing game (CSG). In our proposed game, every
receiving node chooses its respective transmitting nodes and consequently, a
cost is assigned to it according to the power imposed on its chosen
transmitting nodes. We discuss how the network is formed in a decentralized
way, find the action of the nodes in the game and show that, despite being
decentralized, the proposed game converges to a stable solution. To find the
centralized global optimum, which is a benchmark to our decentralized approach,
we use a mixed-integer-liner-program (MILP). Simulation results show that our
proposed decentralized approach outperforms the conventional algorithms in
terms of energy efficiency and social cost while it can address the need for an
incentive for collaboration.
