Inter-cluster Topology Control: An Evolutionary Game Perspective

Topology control (TC) is one of the most important techniques used in wireless ad hoc and sensor networks, the goal of which is to assign appropriate transmission power to each node such that the resulting topology is energy efficient and satisfies some global graph properties such as connectivity. In practical networks, with nodes distributed in clusters generally, setting up links between clusters and maintaining inter-cluster connectivity is important. In this paper, we focus on inter-cluster topology control and examine the following question: if nodes behave in a selfish and bounded rational manner, how does it impact the inter-cluster connectivity and energy consumption in the resulting topologies? To model the complicated interactions among intra-cluster and inter-cluster nodes, we formulate the inter-cluster topology control problem as an evolutionary game and derive the evolutionarily stable strategy (ESS) that no one will deviate from. Moreover, we propose a distributed learning algorithm for the nodes to converge to the ESS. With the proposed algorithm, each node chooses its transmission power with the probabilities learned purely from its own past utility history. Simulation results show that our system can quickly converges to the ESS, which is robust to sudden unfavorable deviations of the selfish nodes.