Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> A major challenge in the operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With the increasing demand for wireless data services, it is necessary to establish power control algorithms for information sources other than voice. We present a power control solution for wireless data in the analytical setting of a game theoretic framework. In this context, the quality of service (QoS) a wireless terminal receives is referred to as the utility and distributed power control is a noncooperative power control game where users maximize their utility. The outcome of the game results in a Nash (1951) equilibrium that is inefficient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the noncooperative power control game, i.e., to obtain improvements in user utilities relative to the case with no pricing. Specifically, we consider a pricing function that is a linear function of the transmit power. The simplicity of the pricing function allows a distributed implementation where the price can be broadcast by the base station to all the terminals. We see that pricing is especially helpful in a heavily loaded system. <s> BIB001 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> We present a game-theoretic treatment of distributed power control in CDMA wireless systems using outage probabilities. We first prove that the noncooperative power control game considered admits a unique Nash equilibrium (NE) for uniformly strictly convex pricing functions and under some technical assumptions on the SIR threshold levels. We then analyze global convergence of continuous-time as well as discrete-time synchronous and asynchronous iterative power update algorithms to the unique NE of the game. Furthermore, we show that a stochastic version of the discrete-time update scheme, which models the uncertainty due to quantization and estimation errors, converges almost surely to the unique NE point. We finally investigate and demonstrate the convergence and robustness properties of these update schemes through simulation studies. <s> BIB002 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> This paper proposes a distributed optimization framework for wireless multihop sensor networks base on a game theoretic approach. We show that the cross-layer optimization problem can be decomposed into two subproblems corresponding to two separate layers (the physical and the application layers) of the overall system. By modelling each subproblem as a noncooperative game, we aim to solve the nonconvex application-layer rate- allocation and physical-layer power-allocation subproblems in a distributed manner. Further, we prove the existence, uniqueness, and stability of the Nash equilibria for both games under certain sufficient conditions. Finally, we show that by using a set of dual variables as the market prices to coordinate the physical layer supply and the application layer demand, the overall optimization process strikes a right balance between the two layers in an overall cross-layer design. <s> BIB003 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> We present a novel formulation of the problem of energy misbehavior and develop an analytical framework for quantifying its impact on other nodes. Specifically, we formulate two versions of the power control problem for wireless sensor networks with latency constraints arising from duty cycle allocations. In the first version, strategic power optimization, nodes are modeled as rational agents in a power game, who strategically adjust their powers to minimize their own energy. In the other version, joint power optimization, sensor nodes adjust their transmission powers to minimize the aggregate energy expenditure. Our analysis of these models yields insight into the different energy outcomes of strategic versus joint power optimization. We show that while joint power optimization fits the accepted paradigm of cooperation among sensor nodes (for example large number of sensor nodes cooperating for a task such as target tracking), it comes with both advantages and disadvantages when energy misbehavior is taken into account. One advantage is that it can (sometimes) be energy-dominant, i.e., the optimal energy cost for each node under joint energy minimization is lower than its strategically optimal energy cost. We then develop a model for characterizing energy misbehavior and show that joint optimization is disadvantageous because it is impossible to prevent misbehavior under any channel quality and load constraints, whereas strategic optimization is more resilient. We prove that it is impossible for a node to unilaterally and undetectably follow a different energy optimization strategy than the other nodes and hence the only threat to the network is misbehavior through false advertisement. We then provide sufficient conditions under which misbehavior through false advertisement can be prevented under a strategic optimization regime. Our analytical results reveal optimal strategies for attacking nodes in an enemy network through energy depletion and help develop effective defense mechanisms for protecting our own wireless network against energy attacks by an intelligent adversary. <s> BIB004 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> We consider a distributed power control scheme for wireless ad hoc networks, in which each user announces a price that reflects compensation paid by other users for their interference. We present an asynchronous distributed algorithm for updating power levels and prices. By relating this algorithm to myopic best response updates in a fictitious game, we are able to characterize convergence using supermodular game theory. Extensions of this algorithm to a multichannel network are also presented, in which users can allocate their power across multiple frequency bands. <s> BIB005 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> Abstract Energy saving is the most important issue in research and development for wireless sensor networks. A power control mechanism can reduce the power consumption of the whole network. Because the character of wireless sensor networks is restrictive energy, this paper proposes a distributed power control algorithm based on game theory for wireless sensor networks which objects of which are reducing power consumption and decreasing overhead and increasing network lifetime. The game theory and OPNET simulation shows that the power control algorithm converges to a Nash Equilibrium when decisions are updated according to a better response dynamic. <s> BIB006 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> Energy harvesting technologies are required for autonomous sensor networks for which using a power source from a fixed utility or manual battery recharging is infeasible. An energy harvesting device (e.g., a solar cell) converts different forms of environmental energy into electricity to be supplied to a sensor node. However, since it can produce energy only at a limited rate, energy saving mechanisms play an important role to reduce energy consumption in a sensor node. In this article we present an overview of the different energy harvesting technologies and the energy saving mechanisms for wireless sensor networks. The related research issues on energy efficiency for sensor networks using energy harvesting technology are then discussed. To this end, we present an optimal energy management policy for a solar-powered sensor node that uses a sleep and wakeup strategy for energy conservation. The problem of determining the sleep and wakeup probabilities is formulated as a bargaining game. The Nash equilibrium is used as the solution of this game. <s> BIB007 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> This paper proposes a cooperation strategy among rational nodes in a wireless cooperative relaying network as an effort to solve two basic problems, i.e., when to cooperate and how to cooperate. First, a symmetric system model comprising two users and an access point (AP) is presented. In this model, each user plays an equal role and acts as a source as well as a potential relay and has the right to decide the amount of bandwidth it should contribute for cooperation. Second, referring to the cooperative game theory, the above problems are formulated as a two-person bargaining problem. Then, a cooperation bandwidth allocation strategy based on the Nash bargaining solution is proposed, in which if a derived condition is satisfied, users will cooperatively work, and each will share a certain fraction of its bandwidth for relaying; otherwise, they will independently work. Simulation results demonstrate that when cooperation takes place, users benefit from the proposed strategy in terms of utility, and those with longer distance to the AP should spend more bandwidth to cooperate with others. <s> BIB008 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> To solve the problem of energy saving in the design of wireless sensor networks(WSN),this paper proposes a power control mechanism based on game theory to reduce power consumption of the whole network.The issue of restrictive energy in WSN was abstractly analyzed,and then the distributed self-adaptive power control algorithm based on game theory was studied through analyses of the mapping between WSN and the game.The results of OPNET simulations show that this algorithm can reduce power consumption,decrease overhead and increase network lifetime.Thus this algorithm can converge to a Nash Equilibrium when decisions are updated according to a better dynamic response and ensure nice fairness for network. <s> BIB009 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <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> BIB010 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <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> BIB011 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> In a Wireless Sensor Network (WSN), the heterogeneous types of sensors can be viewed as intelligent agents that interact with each other locally. The sensors interact with each other either in a cooperative way to form coalitions or in a noncooperative way to deal with conflicts. In this way, the sensors ultimately form desirable topology patterns in terms of various applications. This article addresses the transmit power control problem of sensor networks in the context of two different but related situations: noncooperative game versus cooperative game. Heterogeneity poses challenges to system design of WSN, while practical applications require a distributed power control algorithm to ensure reliability as well as power efficiency. We analyzed the rationales for both assumptions and the corresponding applicability in WSN. The solution concepts in both circumstances are proposed. We study both the utility function for individual nodes and the characteristic function for a coalition to achieve desirable frame success rate and node degree while minimizing the power consumption. We propose power allocation algorithms for network formation resulting from both selfish nodes and cooperative nodes. <s> BIB012 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> In this paper, we study distributed power control in an interference network. In particular, distributed power control mechanisms are devised by exploiting a one-shot non-cooperative game based on a suitably chosen utility function. The utility is a function of quality of service (QoS) objectives defined in terms of fading-induced outage probabilities. Equilibrium analysis of the resulting power control game is made, and its relationship with admission control is discussed. The main contribution of the paper is a mechanism for obtaining smooth non-monotonic reaction curves, in contrast to sharp cut-offs with increasing interference that are characteristic of admission control. This is done via the introduction of a factor ƒ d (.) into the utility function, allowing users to smoothly decrease their objectives in response to interference. The resulting algorithm is called non-monotonic power control (NMPC). We provide sufficient conditions for a unique Nash equilibrium (NE) under NMPC. The equilibria are studied in numerical examples, which exhibit that NMPC increases the number of users who achieve their objectives, without removing any user, as compared to previous utility-based power control algorithms with harsher reaction curves. Considerable energy efficiency is gained by a transfer of resources from the disadvantaged user to the advantaged: users whose SIR objectives are infeasible under current channel gains reduce their own transmit power thus helping on others. We view this solution as an attractive alternative to pricing in wireless networks formed by cooperative nodes (such as sensor networks) where an economic model is not natural. <s> BIB013 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> A wireless sensor network is a network of compact micro-sensors equipped with wireless communication capability. In a wireless sensor network deployed to collect and update data, sensor nodes are usually battery-powered. Moreover, they are hardly able to support complex computation. Such unique features give rise to a critical issue; how to devise a simple energy-aware MAC scheme. Intending to resolve the issue, we consider a MAC scheme based on p-persistence slotted ALOHA. To determine the value of the attempt probability p, we construct the p-persistence slotted ALOHA as a simple non-cooperative game which involves generalized payoffs reflecting energy saving and throughput. Then, we derive a Nash equilibrium in a closed form. A Nash equilibrium is known to possibly incur a protocol failure and network instability. Using the Nash equilibrium, we thus investigate the effect of the payoffs on the stability of a wireless sensor network. For the stability of the wireless sensor network, numerical examples suggest an appropriate reflection of the traffic load on the payoffs. <s> BIB014 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> Using cooperative game theory,a cooperative communication scheme is studied for wireless sensor networks.In the proposed system,each user node can act as a source as well as a potential relay,and is willing to achieve an optimal signal-to-noise ratio(SNR) increase by adjusting the power value it should contribute to cooperative relaying.The power allocation problem is modeled as a two-person bargaining game.And the Nash bargaining solution(NBS) is used to achieve a win-win strategy for the cooperative nodes.Simulation results indicate that the NBS resource sharing is fair in that the degree of cooperation of a node only depends on how much contribution its partner can make to its SNR increase. <s> BIB015 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> This paper proposes a cooperative strategy for multi-user symmetrical cooperative communication networks. The cooperative strategy for two users is not suitable for the multi-user networks, where only part of the users participate in cooperation. To solve this problem, first, a multi-user cooperative framework executed in turn is presented and the cooperative condition is established. Second, the users' maximum feasible cooperative subset is obtained via the admission control algorithm. Then, an optimal bandwidth allocation framework is proposed utilizing NBS (Nash bargaining solution) from cooperative game theory. Simulation results demonstrate that the proposed strategy could find the users' cooperative subset effectively, and obtain better transmission rates than the non-cooperative strategy. <s> BIB016 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> Current advances in wireless sensor networks have contributed to the development of multi-hop wireless body sensor networks (WBSNs). These networks, which are primarily comprised of low-power sensor nodes, provide long term health and physiological monitoring of patients without obstructing their normal activities. However, the time-varying nature of network resources poses a significant challenge to the high reliability of operations required of a body sensor network. In this paper, we address the problem of reliability optimization in multi-hop WBSNs, where the nodes co-operate with each other in maximizing system performance. We model our problem as a co-operative game which inherently induces a distributed mechanism that optimizes the reliability of network operations in a multi-hop WBSN supporting concurrent applications. By the term ‘reliability’, we imply the system utility generated when each sensor node (user) services its specific application. We denote the system utility as an instance of the vector of utilities of individual users, where each user's utility is a function of its allocated bandwidth. Our mechanism jointly accounts for the dynamistic nature of the wireless medium, application quality of service, user fairness in achieving the resources to service applications, and results in an optimal operating point (utility vector) at which the WBSN should operate. We arrive at the result that the Nash bargaining solution of the co-operative game gives us the optimal system operating point, i.e., the Nash bargaining solution optimizes the overall system reliability. <s> BIB017 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> We propose a game-theory-based cross-layer optimization scheme for wireless Direct Sequence Code Division Multiple Access (DS-CDMA) visual sensor networks. The scheme uses the Nash Bargaining Solution (NBS), which assumes that the nodes negotiate, with the help of a centralized control unit, on how to allocate resources. The NBS takes into account the video quality each node could achieve without making an agreement. The cross-layer optimization scheme determines the source coding rate, channel coding rate, and transmission power for each node. We compare the proposed game-theory-based scheme with competing schemes that minimize the average or maximum distortion among the nodes. Experimental results are presented and conclusions are drawn. <s> BIB018 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Power Management-Energy Saving and Power Control <s> The performance in cooperative communication depends on careful resource allocation such as relay selection and power Control. This paper introduces novel concepts for relay selection schemes based on coalitional game theory which establishes the dynamic formation of coalitions in multi user wireless networks. Then we present a power allocation for wireless data transmission among coalition based on a noncooperative game. Through this games theoretical framework, source nodes are able to self organize and form a stable coalitions and set their transmission powers in a completely distributed manner. Numerical results denote that the proposed algorithm achieves significant reduction in energy consumption and improvement in payoff for the users, compared to noncooperative power control approaches. <s> BIB019
In WSN, energy is a limited resource and must be used judiciously. Currently, the energy problem remains one of the major obstacles somehow preventing the complete exploitation of WSN technology. Energy saving and power control strategies should be devised at sensor nodes as well as in the network to prolong the network lifetime. In practice, the Game-theoretical Total Link (GTL) algorithm which sets each node's energy range is usually better than Critical Transmitting Range (CTR) in energy saving according to the topological changing, as shown by Zhang et al.  . Kyung et al. BIB014 considered a MAC scheme based on p-persistence slotted ALOHA. To determine the value of the attempt probability p, the authors constructed the p-persistence slotted ALOHA as a simple non-cooperative game which involves generalized payoffs reflecting energy saving and throughput. They derived an NE in a closed form. Zhang et al. BIB015 investigated a cooperative communication scheme for WSN. They modeled the power allocation problem as a two-person bargaining game, and used the Nash Bargaining Solution (NBS) BIB015 BIB010 BIB011 BIB016 BIB017  BIB018 BIB008  ] to achieve a win-win strategy. A distributed optimization framework using GT was used to analyze the power-allocation and rate allocation in WSNs BIB003 . Na et al. BIB006 proposed a distributed power control algorithm based on game theory for WSN, and its objectives are formulated toward reducing power consumption, decreasing overhead and increasing network lifetime. The simulation shows that this power control algorithm converges to a NE when decisions are updated according to a better response dynamic. The heterogeneous types of sensors are viewed as intelligent agents interacting with each other locally in a WSN. Sensors in this network interact with each other either in a cooperative way to form coalitions or in a non-cooperative way to deal with conflicts. Ren et al. BIB012 addressed non-cooperative game and cooperative game in a distributed power control algorithm to ensure reliability as well as power efficiency by proposing power allocation algorithms for network formation resulting from both selfish nodes and cooperative nodes. The contribution in BIB013 has a mechanism for obtaining smooth non-monotonic reaction curves, in contrast to sharp cut-offs with increasing interference that are characteristic of admission control. They BIB013 provided sufficient conditions for a unique NE under non-monotonic power control (NMPC) algorithm, and view this solution as edan attractive alternative to pricing in wireless networks formed by cooperative nodes. Alpcan et al. BIB002 presented a game-theoretic treatment of distributed power control in CDMA wireless systems using outage probabilities and proved that the non-cooperative power control game considered admits a unique NE for uniformly strictly convex pricing functions and under some technical assumptions on the SIR threshold levels. Chen et al. BIB009 proposed a power control mechanism based on game theory to reduce power consumption of a WSN. The issue of restrictive energy in WSN was abstractly analyzed, and then the distributed self-adaptive power control algorithm was studied by analyzing the mapping between WSN and the game. The algorithm can reduce power consumption, decrease overhead and increase network lifetime, and converge to a NE when decisions are updated according to a better dynamic response and ensure nice fairness for network. Kannan et al. BIB004 presented a novel formulation of the problem of energy misbehavior and develop an analytical framework for quantifying its impact on other nodes. They formulated two versions of the power control problem for WSN with latency constraints arising from duty cycle allocations. In the first version, strategic power optimization, nodes are modeled as rational agents in a power game, who strategically adjust their powers to minimize their own energy. In the other version, joint power optimization, sensor nodes adjust their transmission powers to minimize the aggregate energy expenditure. Khayatian et al. BIB019 introduced novel concepts for relay selection schemes based on coalitional game theory which establishes the dynamic formation of coalitions in multi-user wireless networks and present a power allocation for wireless data transmission among coalition based on a non-cooperative game. Through this games theoretical framework, source nodes are able to self organize and form a stable coalition, and set their transmission powers in a completely distributed manner. Niyato et al. BIB007 presented an optimal energy management policy for a solar-powered sensor node that uses a sleep and wakeup strategy for energy conservation. The problem of determining sleep and wakeup probabilities is formulated as a bargaining game. Moreover, NE is used as the solution of this game. Huang et al. BIB005 presented a pricing-based distributed power control scheme to compensate interference in sensor networks, inspired by the non-cooperative power control game studied in BIB001 . The misbehavior of terminals would create a social-dilemma where terminals exhibit uncertainty about the cooperative behavior of other terminals in the network. Cooperation in social-dilemma is characterized by a sub-optimal NE where wireless terminals opt out of cooperation. To maintain a socially optimal cooperation, a mechanism should be established to detect and mitigate effects of mis-behavior.