Topology control algorithms allow each node in a wireless multi-hop network to adjust the power at which it makes its transmissions and choose the set of neighbors with which it communicates directly, while preserving global goals such as connectivity or coverage. This allows each node to conserve energy and contribute to increasing the lifetime of the network. In this paper, in contrast to most previous work, we consider (i) both the energy costs of communication as well as the amount of available energy at each node, (ii) the realistic situation of varying rates of energy consumption at different nodes, and (iii) the fact that co-operation between nodes, where some nodes make a sacrifice by increasing energy consumption to help other nodes reduce their consumption, can be used to extend network lifetime. This paper introduces a new distributed topology control algorithm, called the Cooperative Topology Control with Adaptation (CTCA), based on a game-theoretic approach that maps the problem of maximizing the network's lifetime into an ordinal potential game. We prove the existence of a Nash equilibrium for the game. Our simulation results indicate that the CTCA algorithm extends the life of a network by more than 50 compared to the best previously-known algorithm. We also study the performance of the distributed CTCA algorithm in comparison to an optimal centralized algorithm as a function of the communication ranges of nodes and node density.
Wireless sensor networks (WSNs) comprising of tiny, power-constrained nodes are gaining popularity due to their potential for use in a wide variety of environments like monitoring of environmental attributes, intrusion detection, and various military and civilian applications. While the sensing objectives of these environments are unique and application-dependent, a common performance criteria for wireless sensor networks is prolonging network lifetime while satisfying coverage and connectivity in the deployment region. Security is another important performance parameter in wireless sensor networks, where adverse and remote environments pose various kinds of threats to reliable network operation. In this paper, we look at the problems of security and energy efficiency and different formulations of these problems based on the approach of game theory. The potential applicability of WSNs to intruder detection environments also lends itself to game-theoretic formulation of these environments, where pursuit-evasion games provide a relevant framework to model detection, tracking and surveillance applications. The suitability of using game theory to study security and energy efficiency problems and pursuit-evasion scenarios using WSNs stems from the nature of strategic interactions between nodes. Approaches from game theory can be used to optimize node-level as well as network-wide performance by exploiting the distributed decision-making capabilities of WSNs. The use of game theory has proliferated, with a wide range of applications in wireless sensor networking. In the wake of this proliferation, we survey the use of game-theoretic approaches to formulate problems related to security and energy efficiency in wireless sensor networks. Large-scale, self-organizing wireless sensor and mesh network deployments are being driven by recent technological developments such as The Internet of Things (IoT), Smart Grids and Smart Environment applications. Efficient use of the limited energy resources of wireless sensor network (WSN) nodes is critically important to support these advances, and application of topology control methods will have a profound impact on energy efficiency and hence battery lifetime. In this survey, we focus on the energy efficiency issue and present a comprehensive study of topology control techniques for extending the lifetime of battery powered WSNs. First, we review the significant topology control algorithms to provide insights into how energy efficiency is achieved by design. Further, these algorithms are classified according to the energy conservation approach they adopt, and evaluated by the trade-offs they offer to aid designers in selecting a technique that best suits their applications. Since the concept of "network lifetime" is widely used for assessing the algorithms' performance, we highlight various definitions of the term and discuss their merits and drawbacks. Recently, there has been growing interest in algorithms for non-planar topologies such as deployments in underwater environments or multi-level buildings. For this reason, we also include a detailed discussion of topology control algorithms that work efficiently in three dimensions. Based on the outcomes of our review, we identify a number of open research issues for achieving energy efficiency through topology control.  Topology Control (TC) is one of the most important techniques used in wireless ad hoc and sensor networks to reduce energy consumption (which is essential to extend the network operational time) and radio interference (with a positive effect on the network traffic carrying capacity). The goal of this technique is to control the topology of the graph representing the communication links between network nodes with the purpose of maintaining some global graph property (e.g., connectivity), while reducing energy consumption and or interference that are strictly related to the nodes' transmitting range. In this article, we state several problems related to topology control in wireless ad hoc and sensor networks, and we survey state-of-the-art solutions which have been proposed to tackle them. We also outline several directions for further research which we hope will motivate researchers to undertake additional studies in this field.