Cost Sharing Games for Energy-Efficient Multi-Hop Broadcast in Wireless Networks

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.