Game Theory for Wireless Sensor Networks: A Survey <s> Repeated Game Theory <s> CSMA/CA protocols rely on the random deferment of packet transmissions. Like most other protocols, CSMA/CA was designed with the assumption that the nodes would play by the rules. This can be dangerous, since the nodes themselves control their random deferment. Indeed, with the higher programmability of the network adapters, the temptation to tamper with the software or firmware is likely to grow; by doing so, a user could obtain a much larger share of the available bandwidth at the expense of other users. We use a game-theoretic approach to investigate the problem of the selfish behavior of nodes in CSMA/CA networks, specifically geared towards the most widely accepted protocol in this class of protocols, IEEE 802.11. We characterize two families of Nash equilibria in a single stage game, one of which always results in a network collapse. We argue that this result provides an incentive for cheaters to cooperate with each other. Explicit cooperation among nodes is clearly impractical. By applying the model of dynamic games borrowed from game theory, we derive the conditions for the stable and optimal functioning of a population of cheaters. We use this insight to develop a simple, localized and distributed protocol that successfully guides multiple selfish nodes to a Pareto-optimal Nash equilibrium. <s> BIB001 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Repeated Game Theory <s> Focusing on dropping packets attacks in sensor networks, we propose a model of dropping packets attack-resistance as a repeated game based on such an assumption that sensor nodes are rational. The model prevents malicious nodes from attacking by establishing punishment mechanism, and impels sensor networks to reach a collaborative Nash equilibrium. Simulation results show that the devised model can effectively resist the dropping packets attacks(DPA) by choosing reasonable configuration parameters. <s> BIB002 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Repeated Game Theory <s> In wireless ad hoc networks, autonomous nodes are reluctant to forward others' packets because of the nodes' limited energy. However, such selfishness and noncooperation deteriorate both the system efficiency and nodes' performances. Moreover, the distributed nodes with only local information may not know the cooperation point, even if they are willing to cooperate. Hence, it is crucial to design a distributed mechanism for enforcing and learning the cooperation among the greedy nodes in packet forwarding. In this paper, we propose a self- learning repeated-game framework to overcome the problem and achieve the design goal. We employ self-transmission efficiency as the utility function of individual autonomous node. The self transmission efficiency is defined as the ratio of the power for self packet transmission over the total power for self packet transmission and packet forwarding. Then, we propose a framework to search for good cooperation points and maintain the cooperation among selfish nodes. The framework has two steps: First, an adaptive repeated game scheme is designed to ensure the cooperation among nodes for the current cooperative packet forwarding probabilities. Second, self-learning algorithms are employed to find the better cooperation probabilities that are feasible and benefit all nodes. We propose three learning schemes for different information structures, namely, learning with perfect observability, learning through flooding, and learning through utility prediction. Starting from noncooperation, the above two steps are employed iteratively, so that better cooperating points can be achieved and maintained in each iteration. From the simulations, the proposed framework is able to enforce cooperation among distributed selfish nodes and the proposed learning schemes achieve 70% to 98% performance efficiency compared to that of the optimal solution. <s> BIB003 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Repeated Game Theory <s> The lack of cooperation among the nodes of a network may seriously affect the network functions.In order to solve the problem,a repeated game framework,which optimizes packet forwarding probabilities of distributed nodes by detecting and re- sponding the selfish behavior,is proposed.By the repeated game among nodes and broadcasting the monitored nodes’utility change,the framework could detect the selfish behavior in the network in time.A punishing mechanism which prevents the selfish nodes’deviation from cooperation is provided.The simulation results show that with the punishment mechanism in the model, selfish nodes can be forced to participate to the network operation and maintain the connectivity of network. <s> BIB004 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Repeated Game Theory <s> Energy consumption, path reliability and node’s life time are the key issues in wireless sensor network routing. We present a repeated game theoretic model based on cooperative packet forwarding under the conditions of selfish and rational nodes for improving energy efficiency and sensor networks payoff, we also design a payoff function on path reliability and energy consumption. Using the punishment mechanism, the repeated game model can propel a Nash Equilibrium and decrease the defection possibility of selfish nodes. The simulation results show that the repeated game model enhances the network payoff and increases the network throughput, and also show that the defection at any selfish node will degrade the network payoff and cause energy waste. <s> BIB005 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Repeated Game Theory <s> In this paper, we study the selfish behavior in wireless sensor networks and apply a game theory method to address this problem in a CSMA/CA protocol. More specifically, we formulate the Media Access Control (MAC) layer activity in sensor networks as an optimization problem in terms of the random accessing problem. Then we propose a distributed algorithm for the system to reach the Nash Equilibrium (NE). We have de-fined a Contention Window Select Game (CWSG) in which each sensor selects its own contention window to control the access probability. This approach can improve the average performance, compared to a random strategy with each sensor selecting its own window independently. We prove the unique existence of NE in the CWSG, and propose a penalizing mechan-ism based on repeated game to prevent the non-cooperative selfish behavior of decreasing the contention window without per-mission. <s> BIB006
Repeated game theory is an extensive form game theory BIB001 , a player has to take into account the impact of its current action on the future actions of others. Agah and Das [100] studied a repeated game formulation between malicious sensor nodes and an intrusion detector in the case of preventing passive Denial of Services (DoS) attacks at routing layer in WSN. Yang et al. BIB002 tackled the problem of dropping packets attacks in WSN, and modeled the interactions among sensor nodes as a repeated game. Xidong et al.  applied game theoretic dynamic power management policy for distributed WSN using repeated games. Yan et al. BIB006 defined a Contention Window Select Game (CWSG) in which each sensor node selects its own contention window to control the access probability, and proved the unique existence of NE in the CSWG. A penalizing mechanism based on repeated game theory to prevent the non-cooperative selfish behavior of decreasing the contention window without permission was proposed. Liu et al. BIB005 suggested a repeated game theoretic model. The model is based on cooperative packet forwarding under the conditions of selfish and rational nodes for improving energy efficiency and sensor networks payoff. The authors also formulated a payoff function on path reliability and energy consumption. Using the punishment mechanism, this repeated game model can propel a NE and decrease the defection possibility of selfish nodes. Pandana et al. BIB003 developed a self-learning repeated-game framework to enforce and learn the cooperation among the greedy nodes in packet forwarding. Zhou et al. BIB004 proposed a repeated game framework with a punishment mechanism to optimize packet forwarding probabilities by detecting, responding and punishing the nodes having selfish behaviors.