On Selfishness, Local Information, and Network Optimality: A Topology Control Example

Topology control of ad hoc and mesh networks specifies how to assign per-node transmission parameters (such as power level, frequency etc.) so as to achieve energy efficiency, while maintaining certain desirable properties such as connectivity. In autonomous networks, nodes may act in their self- interest and improve their performance, perhaps at the expense of other nodes´, or even the overall network´s, performance. Besides, nodes must also contend with limited information about the network operating state during their decision-making. We analyze the above problem using non-cooperative game theory and quantify the impact of partial network state knowledge that nodes possess on the network optimality. We develop a local topology control algorithm that uses the idea of maintaining connectivity of 1-hop neighborhoods. This algorithm is first shown to converge and be stable. We then examine the trade-off between network performance (energy efficiency) and the cost of having knowledge (by exchanging control messages): more information exchange makes the nodes more network-aware, and hence leads to more efficient networks, but exchange of control information itself is costly. Taking the cost of obtaining knowledge into account, we observe that when nodes can operate along the continuum of knowledge, from 1-hop to omniscience, the network consumes least energy when nodes have significantly less connectivity information.