  We study multi-hop broadcast in wireless networks with one source node and
multiple receiving nodes. The message flow from the source to the receivers can
be modeled as a tree-graph, called broadcast-tree. The problem of finding the
minimum-power broadcast-tree (MPBT) is NP-complete. Unlike most of the existing
centralized approaches, we propose a decentralized algorithm, based on a
non-cooperative cost-sharing game. In this game, every receiving node, as a
player, chooses another node of the network as its respective transmitting node
for receiving the message. Consequently, a cost is assigned to the receiving
node based on the power imposed on its chosen transmitting node. In our model,
the total required power at a transmitting node consists of (i) the transmit
power and (ii) the circuitry power needed for communication hardware modules.
We develop our algorithm using the marginal contribution (MC) cost-sharing
scheme and show that the optimum broadcast-tree is always a Nash equilibrium
(NE) of the game. Simulation results demonstrate that our proposed algorithm
outperforms conventional algorithms for the MPBT problem. Besides, we show that
the circuitry power, which is usually ignored by existing algorithms,
significantly impacts the energy-efficiency of the network.
