Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> We describe a decentralized learning-based activation algorithm for a ZigBee-enabled unattended ground sensor network. Sensor nodes learn to monitor their environment in a low-power "sleep" mode, until an intruder is detected, then enter a full-power mode only if the benefit for doing so outweighs an energy cost. Our formulation accounts for the energy required to transmit and the probability of successful transmission in a crowded ZigBee network. Since these depend on the activity of other nodes, we propose a decentralized adaptive algorithm for sensor activation based on game theoretic principles. We show that the algorithm tracks the time-varying set of correlated equilibria of the problem, and illustrate performance through simulation. The algorithm is described as a stochastic approximation, with attendant differential inclusion analysis. <s> BIB001 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> "Introduction to the Theory of Cooperative Games" systematically studies the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games, and the core, the Shapley value, and the ordinal bargaining set of NTU games. To each solution, a separate chapter is devoted, in which its properties are investigated in full detail. Moreover, important variants are defined or even intensively analyzed. Separate chapters cover continuity, dynamics, and geometric properties of solutions of TU games. This study culminates in uniform and coherent axiomatizations of all the foregoing solutions (excluding the bargaining set). Except for the Shapley value such axiomatizations have not appeared in any book. Moreover, "Introduction to the Theory of Cooperative Games" contains a detailed analysis of the main results on cooperative games without side payments. Such analysis is very limited or non-existent in the existing literature on game theory. <s> BIB002 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> 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. <s> BIB003 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> In this tutorial, we provided a comprehensive overview of coalitional game theory, and its usage in wireless and communication networks. For this purpose, we introduced a novel classification of coalitional games by grouping the sparse literature into three distinct classes of games: canonical coalitional games, coalition formation games, and coalitional graph games. For each class, we explained in details the fundamental properties, discussed the main solution concepts, and provided an in-depth analysis of the methodologies and approaches for using these games in both game theory and communication applications. The presented applications have been carefully selected from a broad range of areas spanning a diverse number of research problems. The tutorial also sheds light on future opportunities for using the strong analytical tool of coalitional games in a number of applications. In a nutshell, this article fills a void in existing communications literature, by providing a novel tutorial on applying coalitional game theory in communication networks through comprehensive theory and technical details as well as through practical examples drawn from both game theory and communication application. <s> BIB004 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> The problem of detecting malicious nodes in wireless sensor networks is considered. Since current security mechanisms are inadequate for wireless sensor networks, we must develop a new framework to detect malicious nodes using Zero-Sum game approach and selective node acknowledgements in the forward data path. The first few sections of the paper provide a game model with probability of cost required to defend the nodes and the subsequent sections derives the model to detect malicious nodes using the probability of acknowledgment at source. <s> BIB005 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> Impulse radio-ultra wideband (IR-UWB) communication is a strong candidate for short-range biomedical wireless sensor networks (BWSN). In this paper, we propose a multiband/multiuser IR-UWB scheme, which is robust against unknown narrowband interference (NBI), by deploying multiband signaling with forward error correction (FEC) coding and subband scheduling. We define our problem with an n-transmitter Jamming game and find a Nash equilibrium (NE) for such a game. By the NE result we say that a uniform access to all the subband resources from all the sensors can form a fair situation for the system. In addition, we propose a fair subband scheduling that is required to provide each sensor with uniform opportunity of avoiding the unknown NBI. We cast the problem of finding the fair subband schedule into a multi-objective integer programming, and plan to solve it using Nash bargaining solutions (NBS). <s> BIB006 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> Impulse radio ultra-wideband (IR-UWB) communication is a strong candidate for short range wireless sensor networks (BWSN). One of the biggest challenges in IR-UWB is to suppress the performance degradation due to concurrent narrowband interferences (NBIs). There are two main possible ways of NBI suppression, namely, cancellation and avoidance. The former is difficult to be implemented since it makes receivers largely complicate (e.g., high speed sampling and Rake receivers), and the latter requires accurate detection of NBI center frequency. In this paper we consider a multiuser multiband IR-UWB where no NBI detection mechanism is available due to complexity constraints of implanted biomedical sensors. In this situation, we are interested in finding a transmission scheduling policy that provides a stable state where no single sensor deviates from the scheduling. To this end, we model multiuser multiband IR-UWB as n-transmitter jammer game, and computes its Nash equilibrium that corresponds to the definition of the stable state. We observe that the steady state based on the Nash equilibrium provides a scheduling with the policy of letting all sensors access to all available subbands uniformly. We evaluate the scheduling scheme based on the steady state by comparing it with non-uniform random access scheduling. <s> BIB007 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> Traditional distributed source coding rarely considers the possible link between separate encoders. However, the broadcast nature of wireless communication in sensor networks provides a free gossip mechanism which can be used to simplify encoding/decoding and reduce transmission power. Using this broadcast advantage, we present a new two-encoder scheme which imitates the ping-pong game and has a successive approximation structure. For the quadratic Gaussian case, we prove that this scheme is successively refinable on the {sum-rate, distortion pair} surface, which is characterized by the rate-distortion region of the distributed two-encoder source coding. A potential energy saving over conventional distributed coding is also illustrated. This ping-pong distributed coding idea can be extended to the multiple encoder case and provides the theoretical foundation for a new class of distributed image coding method in wireless scenarios. <s> BIB008 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> In this paper, we propose a game-theoretical based method to fortify an intrusion detection system (IDS) in Wireless Sensor Networks (WSNs). And we focus on dropping-packet attacks which are the sore point in wireless sensor networks. We claim that of course our model is not only a detective model but also a correctional model. because first we corner malicious nodes and then we give them incentives to mend their ways and try to behave in favor of other nodes in WSN. We formulate the attack-defense problem as a non-cooperative, two-player, non-zero-sum game between an attacker and a WSN. We propose a repeated game model of dropping packets which is attack-proof against DPA based on such an assumption that sensor nodes are rational. The model prevents malicious nodes from attacking by establishing subgame perfect periodic collusion-resistant punishment mechanism, and impels sensor networks to reach a cooperative Nash equilibrium. So, it leads to a defense strategy for the network. And when the malicious nodes populate less than the majority of network we show that our model is partially collusion resistant. And even we try to use the sporadic well-mannered cooperative behavior of the malicious node in favor of improving overall throughput of our WSN. Based on rationality we believe that even malicious nodes before being known as extreme notorious nodes, they try to impersonate their true type and show a little collaborative behavior. <s> BIB009 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Motivation <s> Wireless Sensor Networks (WSNs) are becoming an integral part of our lives. There are not widespread applications of WSNs without ensuring WSNs security. Due to the limited capabilities of sensor nodes in terms of computation, communication, and energy, providing security to WSNs is challenging. In fact, the process of implementing WSNs security is adaptive and dynamic, which evolves continually. The essence of attack-defend in WSNs security can be expressed by mutual strategies of interdependence while game theory can be used for the purpose of accounting for interactions among strategies of rational decision makers. Therefore, studying WSNs security with game theory has higher scientificity and rationality. This paper presents a survey of security approaches based on game theory in WSNs. According to different applications, a taxonomy is proposed, which divides current existing typical game-theoretic approaches for WSNs security into four categories: preventing Denial of Services (DoS) attacks, intrusion detection, strengthening security, and coexistence with malicious sensor nodes. The main ideas of each approach are overviewed while advantages and disadvantages of various approaches are discussed. Then, this paper overviews related work and highlights the difference from other surveys, and points out some future research areas for ensuring WSNs security based on game theory, including Base Station (BS) credibility, Intrusion Detection System (IDS) efficiency, WSNs mobility, WSNs Quality of Service (QoS), real-world applicability, energy consumption, sensor nodes learning, and expanding game theory applications and different games. Thus, a global view of WSNs security approaches based on game theory is provided. To our best knowledge of knowing, it is the first paper centrally focusing on game theory in WSNs security. It will make the researchers a better understanding of game-theoretic solutions to WSNs security and further research directions. <s> BIB010
With the rapid development in electronics and wireless technology, WSN will certainly find more and more application when the need for environment sensing arises. On the other hand, the developments of WSN theory and systems have received a lot of attention in both the industry sector and research community. Among many alternative approaches, GT has been increasing applied in the design of WSNs, thus, the scope of this paper is restricted to the use of GT for WSNs. From 2003 to 2011, about 330 research papers with topics on or closely related to GT for WSN were published. Figure 1 shows the yearly distribution of these published papers. The number of records for 2011 is not complete because some publications have not been included in the indexing databases. A relatively smaller portion of the contributions in this area has been summarized in BIB003 BIB010 . Machado and Tekinay BIB003 reviewed 29 publications which mainly focusing on the use of game-theoretic approaches to formulate problems related to security and energy efficiency. Shen et al. BIB010 summarized 30 publications of the existing game theoretical approaches that are designed to strengthen WSN security. Among the variety of developed methods using GT, the main differences and remarkable features can be briefly summarized below. Cooperative game theory provides analytical tools to study the behavior of rational players when they cooperate and consider the utility of all the players BIB004 8] . Non-cooperative game theory also covers a broad range of applications in WSN  BIB001 . In non-cooperative game theory, the nodes buy, sell, and consumer goods in response to the prices that are exhibited in a virtual market. A node attempts to maximize its profit for taking a series of actions. Whether or not a node receives a profit is decided by the success of the action. Note that non-cooperative game theory is mainly focused on each user's individual utility rather than the utility of the whole network. On the contrary, cooperative game theory can achieve general pareto-optimal performance and maximize the entire network's payoff while maintaining fairness. In addition to cooperative and non-cooperative game theories, repeated game theory is concerned with a class of dynamic games, in which a game is played for numerous times and the players can observe the outcome of the previous game before attending the next repetition  . The commonly used GT methods for solving WSN problems are listed in Table 1 . TU game (transferable-utility game) BIB002 (10) NTU game (non-transferable-utility game)  (11) Ping-pong game BIB008 (12) Zero-Sum game and Non-Zero-Sum game BIB005 BIB009 (13) Jamming game BIB006 BIB007 