The problem of topology control is to assign per-node transmission power such that the resulting topology is energy efficient and satisfies certain global properties such as connectivity. The conventional approach to achieve these objectives is based on the fundamental assumption that nodes are socially responsible. We examine the following question: if nodes behave in a selfish manner, how does it impact the overall connectivity and energy consumption in the resulting topologies? We pose the above problem as a noncooperative game and use game-theoretic analysis to address it. We study Nash equilibrium properties of the topology control game and evaluate the efficiency of the induced topology when nodes employ a greedy best response algorithm. We show that even when the nodes have complete information about the network, the steady-state topologies are suboptimal. We propose a modified algorithm based on a better response dynamic and show that this algorithm is guaranteed to converge to energy-efficient and connected topologies. Moreover, the node transmit power levels are more evenly distributed, and the network performance is comparable to that obtained from centralized algorithms.

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This paper examines the problem of topology control in wireless ad-hoc networks. The purpose of topology control is to assign per-node optimal transmission power such that the resulting topology satisfies certain global properties such as connectivity. Due to the multi-hop nature of ad-hoc networks, establishing network connectivity may require nodes to use their power resources to service other nodes. Since nodes have limited power they may act selfishly in order to minimize their power (energy) consumption. Game theory is a suitable tool to analyze the conflicting objectives of nodes seeking to achieve an energyefficient and connected network in the presence of selfish nodes. We present example topology control games and a distributed best response algorithm that together can guarantee convergence to steady state networks satisfying the dual topology control objectives.As a precursor, we analyze formation of a topology that results when nodes interact with each other. In particular, we provide a game theoretic framework for the topology control problem.

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Abstract-In a cognitive network, autonomous and adaptive radios select their operating parameters to achieve individual and network-wide goals. The effectiveness of these adaptations depends on the amount of knowledge about the state of the network that is available to the radios. We examine the price of ignorance in topology control in a cognitive network with power-and spectral-efciency objectives. We propose distributed algorithms that, if radios possess global knowledge, minimize both the maximum transmit power and the spectral footprint of the network. We show that while local (as opposed to global) knowledge has little effect on the maximum transmission power used by the network, it has a signicant effect on the spectral performance. Furthermore, we show that due to the high cost of maintaining network knowledge for highly dynamic networks, the cost/performance tradeoff makes it advantageous for radios to operate under some degree of local knowledge, rather than global knowledge. We also propose distributed algorithms for power and frequency adaptations as radios join or leave the network, and assess how partial knowledge impacts the performance of these adaptations.