Game Theory for Wireless Sensor Networks: A Survey <s> Non-Cooperative Game Theory <s> In wireless sensor networks, where energy of the sensor nodes are finite, power control is an important issue to consider. In this paper, we present a game-theoretic approach to solve the power control problem in CDMA based distributed sensor networks. A non-cooperative game is formulated and the existence of Nash equilibrium is studied for the sensor nodes operating under incomplete information. With the help of this equilibrium, we devise a distributed algorithm for optimal power control and prove that the system is power stable if the nodes comply with certain transmission thresholds. We show that even in the distributed non-cooperative scenario, it is in the best interest of the nodes to remain within these thresholds. The power level at which a node should transmit, to maximize its utility, is also evaluated. Numerical results prove that with the proposed algorithm, the sensor nodes are able to achieve best possible payoff by consuming less power, resulting in extended network lifetime. <s> BIB001 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Non-Cooperative Game Theory <s> When two sponsoring organizations, working towards separate goals, can employ wireless sensor networks for a finite period of time, it can be efficiency-enhancing for the sponsors to program their sensors to cooperate. But if each sensor privately knows whether it can provide a favor in any particular period, and the sponsors cannot contract on ex post payments, then no favors are performed in any Nash equilibrium. Allowing the sponsors to contract on ex post payments, we construct equilibria based on the exchange of "tokens" that yield significant cooperation and increase expected sponsor payoffs. Increasing the sponsors' liability is beneficial because it enables them to use more tokens <s> BIB002 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Non-Cooperative Game Theory <s> Decentralized channel state information is exploited for optimal transmission policies for non-cooperative sensors in wireless networks with the multipacket reception capability. The problem is formulated as a non-cooperative game of a finite number of players and actions with a continuous channel state space. We prove the existence of a Nash equilibrium at which every sensor adopts a threshold policy. A stochastic gradient based algorithm that can be used to adaptively estimate the optimal transmission threshold for a sensor is proposed. The theoretical results and the tracking capability of the algorithm are illustrated via numerical examples <s> BIB003 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Non-Cooperative Game Theory <s> We address the fundamental question of whether or not there exist stable operating points in a network in which selfish nodes share a common channel, and if they exist, how the nodes behave at these stable operating points. We begin with a wireless communication network in which n nodes (agents), which might have different utility functions, contend for access on a common, wireless communication channel. We characterize this distributed multiple-access problem in terms of a one-shot random-access game, and then analyze the behavior of the nodes using the tools of game theory. We give necessary and sufficient conditions on nodes for the complete characterization of the Nash equilibria of this game for all n ≥ 2. We show that all centrally controlled optimal solutions are a subset of this game theoretic solution, and almost all (w.r.t. Lebesgue measure) transmission probability assignments chosen by a central authority are supported by the game theoretic solution. We analyze the behavior of the network throughput at Nash equilibria as a function of the costs of the transmitters incurred by failed transmissions. Finally, we conclude the paper with the asymptotic analysis of the system as the number of transmitters goes to infinity. We show that the asymptotic distribution of the packet arrivals converges in distribution to a Poisson random variable, and the channel throughput converges to - (c/ (1 + c)) In (c/ (1 + c)) with c > 0 being the cost of failed transmissions. We also give the best possible bounds on the rates of convergence of the packet arrival distribution and the channel throughput. <s> BIB004 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Non-Cooperative Game Theory <s> In mobile ad hoc & sensor networks, power control is an efficient way to improve the efficiency of energy. However, it will also produce negative influence on many aspects of the networks such as the network connectivity, delay and network capacity. In this paper, proposed related energy control mechanisms for ad hoc & sensor networks are introduced. Considering the QoS requirement such as maximum network capacity, minimum network radius and guaranteed network connectivity, a power control model based on non-cooperative game theory is given. And a distributed non-cooperative game algorithm to power control for ad hoc & sensor networks is presented. The existing and uniqueness of Nash equilibrium for the algorithm is also proved in this paper. Finally simulation experiments are implemented to verify the algorithm. The results show that the algorithm is efficient and has a good integrated performance. <s> BIB005 </s> Game Theory for Wireless Sensor Networks: A Survey <s> Non-Cooperative Game Theory <s> Sparsely distributed clusters of wireless sensors with applications ranging from state-wide wireless bridge monitoring to animal herds tracking have gained recent attention due to their special characteristics and challenging resource allocation problem. A novel optimal power allocation paradigm based on game theory is proposed to minimize the inter and intra-cluster interference. Cost functions are assigned to the transmission power, estimate of the aggregate interference generated by the cluster on the overall network, and the signal to interference and noise ratio (SINR) at the node level. It is observed that the proposed algorithm demonstrates acceptable convergence properties when used after a channel allocation scheme and is more power efficient if used in parallel with a channel allocation method. Simulation results are presented to support the proposed analysis. <s> BIB006
Non-cooperative game theory studies strategies between interactions among competing players. In the game, a player is called an agent and his goal is to maximize its utility by choosing its strategy individually, in other words, each player is selfish but rational in a non-cooperative game. Non-cooperative game theory uses a utility function to find the NE  BIB004 BIB002 BIB006 BIB003 BIB001 . Non-cooperative game theory is mainly applied in distributed resource allocation, congestion control, power control, spectrum sharing in cognitive radio and many others. With the concepts from economics and game theory, Wu and Wei  proposed a mechanism design to handle incentives of strategic agents. A power control model based on non-cooperative game theory is given in BIB005 .