Network Formation Among Selfish Energy-Constrained Wireless Devices

We study the formation of ad-hoc networks among selfish energy-constrained wireless devices that are primarily interested in being connected with other devices. We use a non-cooperative bilateral connection game (BCG) framework to study network formation. For a BCG in which devices choose their individual strategies to remain connected by minimizing only their direct transmission power costs, we show that the price-of-anarchy is unbounded in the network size. We propose a BCG with an alternate cost structure in which each device additionally pays the transmission power costs incurred by other devices for its own traffic. We show that a unique network structure emerges in this game that is stable as well as socially efficient. We then study the achievable throughput for random point-to-point traffic in this stable energy-efficient network. When the nodes of a network are located in a bounded planar region the distribution of point- to-point flows through the nodes exhibits a scale-free behavior.