The significant scale of the Internet of Things (IoT), in conjunction with its heterogeneous nature since it involves many device types, could lead the IoT to be exposed many security threats and attacks from adversaries. Game theory is a promising tool that can be used to design anti-adversary protection strategies for different network security scenarios. Traditionally, such anti-adversary strategies aim to minimize the expected number of infected/corrupted nodes. A con of such a traditional approach is that, due to limited resources available for defense, the IoT controller might have to sacrifice the protection of some nodes in order to better protect others, thus minimizing the expected number of infected nodes. This could lead to drastic consequences for the protected network as a whole since, by merely changing its behavior, the adversary might succeed with a higher probability of corrupting a few of the nodes, and thereby corrupt the network’s operation as a whole although the total number of infected nodes is reduced. In this paper, motivated by this observation, we suggest using the protection level as a payoff for the IoT controller. Under the protection level metric, we specify a minimal probability of being non-infected for each of the IoT nodes. Finally, we suggest an approach how to combine a strategy that maximizes the protection level strategy with a strategy that minimizes the expected number of infected/corrupted nodes so as to increase the joint efficiency. We provide examples to numerically illustrate the derived strategies.

Due to the open nature of wireless channels, wireless networks are susceptible to various physical layer security threats, including interference from jamming attacks. Such jamming attacks may adversely affect communication and diminish the reliability of receiving essential data and commands. Such communication reliability is crucial when an operator controls mobile objects, as a reduction in the reliability of getting commands or information might lead to drastic consequences. Specifically, we consider a communication center equipped with multiple antennas to communicate with a group of receivers (say, drones) performing missions in separate zones. In each zone for its protection, a jammer is installed to disrupt the communication of the communication center with the corresponding receiver. As a metric of communication reliability, we consider the signal-to-interference-plus-noise ratio (SINR) at the receiver. Since designing an anti-jamming strategy in such a hostile environment involves different agents, such as the communication center and the jammers, each with its own objectives, the problem is modeled within a game-theoretic framework. Traditionally, in such a background, the anti-jamming strategy aims to maximize the total SINR or throughput among all the receivers. A con of such a traditional approach is that, due to limited resources, the communication center might have to sacrifice communication with some receivers to maximize the total communication. This could compromise the joint mission as the receivers (drones) might face a lack of data. Motivated by this observation, we suggest using the minimal SINR among all the receivers as a communication metric for the group of receivers. This metric reflects the guaranteed reliability of communication with each receiver. In particular, we derive and illustrate an anti-jamming strategy in the most critical scenario for the communication node, where the communication node is unaware of the exact locations of the jammers but only their distributions, whereas the jammers know their location exactly.

The shared and open-access nature of wireless technologies makes wireless networks susceptible to interference, such as jamming, that could lead to delays in communication and result in delays with corresponding timely information updates. Such delays in information updates can be crucial when an operator controls mobile objects since their untimely updates might lead to drastic consequences. Specifically, we consider an operator communicating with drones performing a joint mission in a protected zone. The protector (jammer) employs a spherical jamming signal to jam the communication of the operator with the drones to fail their joint mission. To design an anti-jamming strategy in such a scenario involving agents (the operator and the jammer), with different objectives, game theory is employed. Traditionally, in such a background, the anti-jamming strategy aims to minimize the total information freshness reflected by the total delay in information update. A con of such a traditional approach is that, due to limited resources, the operator might have to sacrifice the delay in information update for some drones to minimize the total delay. This could fail the joint drone mission since some drones might follow outdated commands. In this paper, motivated by this observation, we suggest using the guaranteed information freshness metric as a cost function for the operator. Under this metric, we specify the maximal time passed since the last data update for each of the drones. An anti-jamming strategy is derived, and its advantage in comparison with the minimizing total information freshness strategy is illustrated.

Detecting malicious users or unauthorized activities poses a critical challenge in the realm of dynamic spectrum access. Traditionally, in such a problem, an intrusion detection system (IDS) aims to maximize the detection probability. Meanwhile in the networks or radio spectrum problems with multiple nodes or bands, respectively, protocol maximizing detection probability might lead to focusing on scanning the most plausible nodes or bands for intrusion and neglecting to scan less plausible nodes or bands for intrusion due to restricted scanning resources. To deal with this challenge in this paper we suggest a protocol maximizing fairness of detection probabilities among all the bands in the bandwidth. We consider α-fairness as fairness criteria. Moreover, the proposed detection protocol deals with the adversary, who endorses artificial intelligence (AI) enabling the adversary to not only infiltrate the bandwidth without being detected but also to do so in a less predictable manner for the IDS. The problem is modeled and solved in the framework of a two-player game. An advantage of fairness detection probability protocol in comparison with maximizing detection probability protocol is illustrated.

The paper considers a network's communication, where nodes, communicating with a base station, could differ by the access to information they have on their fading channel gain (channel state). Specifically, some of the nodes know their channel states exactly, while other nodes have only statistical state information. Such difference can be motivated by the fact that the channel gain is a function of the distance to the receiver, and some of the nodes might not know their own location, meanwhile, the others might have complete information about their own location via global positioning system (GPS). This scenario is common in IoT networks, particularly those situated in remote or challenging environments where GPS signals may be unreliable or inaccessible. The problem is modeled by a Bayesian game with latency as a communication metric. A novel approach is developed to solve such a heterogeneous problem by access to information in closed form for any number of channel states even for the continuum of them. The uniqueness of equilibrium is proven which reflects the usability of using latency metric and stability in communication based on the suggested communication protocol even when the nodes might differ by access to information about channel states. The equilibrium strategies are numerically illustrated.

In this paper, we model a joint (dual) system maintaining both radar task and communication task under the worst environmental conditions caused by hostile interference of the jammer. This model involves two maxmin problems formulated and solved in zero-sum game framework between system and jammer as players. The first problem is to find the equilibrium power allocation strategy of the system in the spectrum band to maximize communication signal-to-interference-plus-noise ratio (SINR) and radar’s SINR depending on the task the system focuses on. The second problem is to find a trade-off between the expected system’s SINR and fairness in using radar mode and communication mode by the system with $\alpha$-fairness as such criteria. Also, here we consider the jammer as an adversary supporting artificial intelligence (AI) which allows the adversary not just to obstruct the system’s functionality but also might achieve it in a less predictable way for the system. The derived solution is numerically illustrated. Moreover, we suggest an approach allowing us to find an optimal fairness coefficient, in other words, to find the most fair fairness criteria, to support both communication task and radar task.

The paper considers a multi-access channel scenario, where several users communicate with a base station, and investigates power allocation is a game-theoretic framework. The communication metric is the inverse signal-to-interference-plus-noise ratio (SINR) at the base station, which, for low SINR reflects communication delay. Each user faces a trade-off between the latency of the signal received by the base station, and the price that the user pays for using a specific amount of power that causes interference in the system. The equilibrium is derived in closed form and its uniqueness is proven. It is shown that the resulting strategy allows each user to maintain uninterrupted communication. For comparison purposes, we construct a specific three user network scenario, and study the SINR and throughput metrics. In that setting, we show that, unlike the latency metric, SINR and throughput may give rise to multiple equilibria, which may cause destabilization of communication.

We consider the communication between a source (user) and a destination in the presence of a jammer, and study resource assignment in a non-cooperative game theory framework using communication latency as the user's utility. The user switches between two different modes, i.e., the (a) regular transmission mode, according to which both players follow a Nash equilibrium; and the (b) smart transmission mode, according to which the user always implements the best response strategy. First, we consider the case in which the switching between transmission modes occurs with a given frequency. For this case we find the optimal transmission power of the user by formulating and solving a Bayesian game problem. We show that an increase in the frequency of smart transmissions leads to a decrease in communication latency and to an increase in the total transmission cost. We determine the switching frequency that optimizes the latency-cost trade off using α-fairness criteria. We also discuss the implications of the proposed latency metric on the player strategies as compared to the previously well studied signal-to-interference-plus-noise ratio (SINR) metric.

We consider the communication between a source (user) and a destination in the presence of a jammer, and study resource assignment in a non-cooperative game theory framework. A player (the user or the jammer) has incomplete information about its rival's identity in the form of uncertainty; the player only knows the probabilities that its rival is a player implementing a behavioral strategy as a follower in a Stackelberg game (smart-type), or selects a feasible strategy as in a Nash game (regular-type). We model the problem as two Bayesian games. In the first game, the user has incomplete information about the jammer, and in the second game, the jammer has incomplete information about the user. The user's utility is throughput. We prove that a unique equilibrium exists and derive it in closed form as a function of the known probabilities. We show that the Nash and Stackelberg equilibria are boundary cases of the obtained equilibrium. Thus, our approach allows one to incorporate the Nash and Stackelberg equilibria into a unified scale of equilibria. Monotonicity properties of the equilibrium strategies and the corresponding payoffs with respect to the network parameters are proven, and also supported by simulations.

Due to the shared and open-access nature of the wireless medium, wireless networks are vulnerable to jamming attacks. In this paper we study the problem of resource assigning in a single carrier communication system, where a user is communicating with a destination in the presence of a jammer. The jammer's channel to the destination is assumed flat fading, and its gain is known in probabilistic terms. In particular, the jammer's channel gain could take any value out of a finite set, with an a priori known probability. We model the problem in a Bayesian jamming game framework with utility the user throughput. We prove the existence and uniqueness of Nash and Stackelberg equilibria, and derive the equilibrium strategies in closed form. Our theoretical results, also supported by simulations, suggest that the Nash strategy is more sensitive to varying a priori probabilities, as compared to the Stackelberg strategy.

Wireless networks are susceptible to malicious attacks, especially those involving jamming and eavesdropping. To maintain secure and reliable communication under such threats, different anti-adversary strategies have been proposed to mitigate the adversary impact. In this paper, we consider a sophisticated adversary with the dual capability of either eavesdropping passively or jamming any ongoing transmission, and investigate a new aspect to consider when designing an anti-adversary strategy: how uncertainty about whether the rival is rational or subjective could impact the strategies. To model such uncertainty, we formulate a Bayesian Prospect Theory (BPT) extension of the game between a user and an adversary who chooses between an eavesdropping attack and a jamming attack against the user. Meanwhile the user chooses against which of the threats to apply the corresponding best response strategy. Uniqueness of the BPT equilibrium strategies is proven and they are found in closed form.

Due to the shared and open-access nature of the wireless medium, wireless networks are vulnerable to interference in the form of jamming attacks. In the research literature, game theory is a commonly employed tool to describe such jammming attacks as well as to design anti-jamming (defense) strategies. An advantage of such an approach is that it allows one to consider the adversary as a smart agent, who flexibly responds to the action of the other agents. In this paper, we put forward a question: what happen if the rival is smart? How does a priori knowledge about this impact on the rivals strategies. We formulate a jamming problem in a CDMA-style network as a Bayesian game between a jammer and a user with two-sided incomplete information about the type of rival it faces. We prove that the equilibrium exists and is unique. Closed form criteria to establish whether the equilibrium is an inner or boundary equilibrium is established. We derive monotonicity properties for the superposition of the two best response strategies, which allows us to develop an algorithm based on the bisection method to find the fixed point (i.e. equilibrium) of this superposition of best response strategies. Our algorithm can be considered as a learning algorithm since it allows to reduce the zone of uncertainty for the equilibrium by a half per iteration.

Unutilized spectrum, i.e. spectrum holes, are opportunities that may be used for communication or other RF services. In this paper, we explore adversarial attacks that reduce the size of spectrum holes by showing their advantage compared to a random jammer. Using a game-theoretical approach, we design an optimal scanning strategy that provides an increased probability of detecting such an attack. The advantage of our strategy is achieved by focusing scanning efforts on bands that are more likely to be attacked, and neglecting the others. However, such focused scanning is a disadvantage since, if the adversary has a different objective, he can safely sneak usage of the bands neglected by such a specially-tuned spectrum scanner. To deal with this problem, we also derive the optimal scanning allocation that balances between applying the anti-spectrum holes attack scanning strategy and scanning the neglected bands so as to prevent the possibility of the adversary using those bands without being detected.

The problem of ensuring the secrecy of a communication while simultaneously maintaining sufficient throughput is a fundamental challenge facing secret communication. One of the challenges for such problems is that the optimal solution for one of objective might be not optimal for the other (e.g., an increase in secrecy might yield a decrease in throughput). Thus, there is a need for finding a trade-off solution for these objectives. In this paper, we consider a two-step approach to solve such problems and illustrate it for orthogonal frequency-division multiplexing-style communications. In the first step, we use the α-fairness criteria for formulating the tradeoff between objectives. A generalized water-filling equation for this tradeoff problem is solved. This equation includes, as a limit case, the classical case for secret communication with secrecy capacity as payoff. In the second step, we aim to find the best α-fair strategy, and show that Jain's fairness can potentially lead to an unbalanced tradeoff between the two objectives. We arrive at a more balanced tradeoff by means of bargaining over the continuum of α-fair solutions. Both the Nash and Kalai-Smorodinsky bargaining solutions for fulfillment of both objectives are found, and the algorithms for finding the bargaining solutions are derived.

Unutilized spectra, i.e., spectrum holes, are opportunities that may be used for communication or adapting other services that use radio frequency (RF). Such opportunities can also represent an adversarial target, if his objective is to block the RF system from using such opportunities opened by spectrum holes. In this paper, we explore the challenge of finding spectrum holes in an adversarial environment.First, by means of a simple model, we show that an adversary’s attack designed to close spectrum holes can be more harmful for the spectrum holes than just random jamming. This calls for designing a scanning strategy to detect such an attack.Second, by applying a game-theoretical model, we design the optimal scanning strategy to detect such attacks. In particular, we show the efficiency of such a scanning strategy compared with uninformed random scanning. This efficiency is achieved by focusing scanning efforts on the bands that will be more likely under attack, and neglecting less promising bands. Beyond the benefits, though, such a strategy has also drawbacks since, if the adversary has a different objective, such as sneaking usage of the spectrum, he can sneak usage undetected by using the bands neglected by such specially tuned scanning. To deal with this problem,third, we suggest to combine this strategy with a strategy that maximizes detection probability in a learning algorithm that updates the beliefs about the adversary’s objective. The convergence of the combined algorithm is proven.

This paper focuses on the challenge of maintaining reliable connectivity in an ad hoc network, where interference is possible. To cope with such interference, the paper introduces throughput connectivity and weighted throughput connectivity. Throughput connectivity reflects the possibility of establishing communication between nodes for given a signal power level, while weighted throughput connectivity associates the throughput as a weight in the associated network graph. Throughput connectivity is less sensitive to network's parameters than the one based on weighted throughput connectivity. It makes maintaining throughput connectivity protocol less resource consuming (say, by sending less frequently channel state information (CSI)). Whereas, weighted throughput protocol is more efficient in power allocation due to employing a continuous scale in Laplacian matrix. To illustrate these notions, two approaches to maximize connectivity were considered: (a) an adaptive transmission protocol that re-allocates transmission power between nodes, and (b) detecting and eliminating a malicious threat to maintain accumulated connectivity over time slots. The first problem was modeled by a maxmin problem, and solved by Semi-Definite Programming. The second problem was modeled by a stochastic game and solved explicitly.

Abstract Because of the open access nature of wireless communications, wireless networks can suffer from malicious activity, such as jamming attacks, aimed at undermining the network's ability to sustain communication links and acceptable throughput. One important consideration when designing networks is to appropriately tune the network topology and its connectivity so as to support the communication needs of those participating in the network. This paper examines the problem of interference attacks that are intended to harm connectivity and throughput, and illustrates the method of mapping network performance parameters into the metric of topographic connectivity. Specifically, this paper arrives at anti‐jamming strategies aimed at coping with interference attacks through a unified stochastic game. In such a framework, an entity trying to protect a network faces a dilemma: (i) the underlying motivations for the adversary can be quite varied, which depends largely on the network's characteristics such as power and distance; (ii) the metrics for such an attack can be incomparable (e.g., network connectivity and total throughput). To deal with the problem of such incomparable metrics, this paper proposes using the attack's expected duration as a unifying metric to compare distinct attack metrics because a longer‐duration of unsuccessful attack assumes a higher cost. Based on this common metric, a mechanism of maxmin selection for an attack prevention strategy is suggested. Copyright © 2017 John Wiley & Sons, Ltd.

The security community has witnessed a significant increase in the number of different types of security threats. This situation calls for the design of new techniques that can be incorporated into security protocols to meet these challenges successfully. An important tool for developing new security protocols as well as estimating their effectiveness is game theory. This game theory framework usually involves two players or agents: 1) a protector and 2) an adversary, and two patterns of agent behavior are considered: 1) selfish behavior, where each of the agents wants to maximize his payoff; and 2) leader and follower behavior, where one agent (the leader) expects that the other agent (the follower) will respond to the leader's strategy. Such an approach assumes that the agents agree on which strategy to apply in advance. In this paper, this strong assumption is relaxed. Namely, the following question is considered: what happens if it is unknown a priori what pattern of behavior the adversary is going to use, or in other words, it is not known, what game he intends to play? Using a simple game-theoretic model, it is shown that the protector can lose if he does not take into account the possibility that the adversary can play a game other than the one the protector has in mind. Further considered is a repeated game in which the protector can learn about the presence of an adversary, and the behavior of belief probabilities is analyzed in this setting.

When an adversary illicitly uses spectrum that it is not authorized for, it does so with a purpose in mind, such as to download a file or perhaps engage in a real-time communication session. In this paper, we examine how the incorporation of knowledge related to an adversary's purpose can improve the effectiveness of spectrum scanning protocols. First, we study the difference in the thief's behavior when considering throughput and delay as the two primary QoS parameters he is concerned with. Through our analysis, we show that the detection probability of unlicensed access to spectrum resources depends on the application type. Knowledge of the application type can be incorporated to spectrum scanning to tune better it to detect the thief. To illustrate this, we examine two Bayesian games. In the first game, the scanner wants to minimize the time needed to detect the invader. In the second game, the scanner wants to maximize the detection probability at each time slot by adapting its belief regarding the adversary's activity. In particular, it is shown in the minimizing detection time game that the equilibrium strategies are continuous with respect to priori knowledge of the invader's activity. Meanwhile, for the maximizing detection probability game, the strategies can have a jump discontinuity. This phenomena can be explained as the difference between tactical and strategic decision making: tactical decision making allows short-term, unpredictable moves, while strategic decision making is inclined to predictable moves. Finally, since the bandwidth model used in this paper is general, the conclusion as well as the approach provided can be applied to a variety of different network protection problems.

Secret and reliable communication presents a challenge involving a double dilemma for a user and an adversary. One challenge for the adversary is to decide between jamming and eavesdropping. While jamming can be quite effective in preventing reliable communication of the user, it can also be quite harmful for the adversary since he/she can be detected. On the other hand, eavesdropping is quite safe for the adversary; however, it sometimes may not be so efficient compared to jamming, if the adversary cannot respond to the information gleaned from eavesdropping in a timely manner. The user can either transmit, thus becoming vulnerable to malicious activity, or be in a silent mode in turn delaying his/her transmission. However, by combining these modes properly the user can assist an intruder detection system in detecting the adversary, since transmission can provoke the adversary into a jamming attack, and a strategically allocated silent mode while the jammer continues jamming can increase the probability of detecting the adversary. In this paper, to get insight into this problem, two simple stochastic games are proposed. Explicit solutions are found that lead to the characterization of some interesting properties. In particular, it is shown that under certain conditions, incorporating in the transmission protocol a time slot dealing just with the detection of malicious threats can improve the secrecy and reliability of the communication without extra transmission delay.

Detecting malicious users in dynamic spectrum access scenarios is a crucial problem that requires an intrusion detection system (IDS) that scans spectrum for malicious activities. In this paper we design a spectrum scanning protocol that incorporates knowledge about the scanning effectiveness across different bands, which can increase scanning efficiency. The adversary, however, can also exploit such knowledge to its advantage. To understand the interplay underlying this problem, we formulate a Bayesian model, where the IDS faces a scanning allocation dilemma: if the intruder has no knowledge, then all the bands are under equal threat, while if the intruder has complete knowledge, then less-protected bands are more likely to be threatened. We solve this dilemma and show the optimal IDS strategy switches between the optimal response to these threats. Finally, we show that the strategy might be sensitive to prior knowledge, which can be corrected by adapted learning.

The reliable coordination of communication channels between two organizations is becoming an increasingly important problem as we move toward cognitive radio systems that support dynamic spectrum access. The benefit of such coordination is clear in scenarios when both participants are completely benign, but such benefits can be easily negated if one of the participants operates in a manner contrary to their channel assignment. In this paper, we develop and explore a maxmin transmission protocol for a primary user (PU) in a multiband wireless network, where the secondary user (SU) may be malicious and have an intent to cause interference. In this case, the threat that a SU may be an adversary changes the problem and places the PU in a dilemma: 1) if the SU is an adversary then to decrease the probability of interference it is better for the PU to select which channels it uses from a larger set of bands (i.e., possibly even including the bands reserved for the SU) and 2) if the SU turns out to be law obedient, then using a larger set of bands leads to an increased chance of being interfered with. Similarly, the SU also faces a dilemma if he is malicious: if the PU thinks that the SU is law obedient, then to increase the probability of jamming, the SU should target only the bands reserved for the PU; while, if the PU thinks that the SU is malicious, then by switching to the bands reserved for the SU, the probability of interference can be significantly or even totally reduced. Using game-theoretical tools, we formally explore these dilemmas and use the resulting analysis to explore the tradeoffs between different strategies in terms of payoffs to each user and knowledge of the SU's characteristics.

Network security against possible attacks involves making decisions under uncertainty. Not only may one be ignorant of the place, the power, or the time of potential attacks, one may also be largely ignorant of the attacker's purpose. To illustrate this phenomenon, this paper proposes a simple Bayesian game-theoretic model of allocating defensive (scanning) effort among nodes of a network in which a network's defender does not know the adversary's motivation for intruding on the network, e.g., to bring the maximal damage to the network (for example, to steal credit card numbers or information on bank accounts stored there) or to infiltrate the network for other purposes (for example, to corrupt nodes for a further distributed denial of service botnet attack on servers). Due to limited defensive capabilities, the defender faces the dilemma of either: 1) focusing on increasing defense of the most valuable nodes, and in turn, increasing the chance for the adversary to sneak into the network through less valuable nodes or 2) taking care of defense of all the nodes, and in turn, reducing the level of defense of the most valuable ones. An explicit solution to this dilemma is suggested based on the information available to the defender, and it is shown how this information allows the authorities to increase the efficiency of a network's defense. Some interesting properties of the rivals' strategies are presented. Notably, the adversary's strategy has a node-sharing structure and the adversary's payoffs have a discontinuous dependence on the probability of the attack's type. This discontinuity implies that the defender has to take into account the human factor since some threshold values of this inclination in the adversary's behavior could make the defender's policy very sensitive to small perturbations, while in other situations it produces minimal impact.

We consider the game where Alice wants to communicate with Bob secretely, while Eve wants to hinder this objective by either eavesdropping or jamming, though she cannot employ both eavesdropping and jamming simultaneously. Alice is employing a multi-channel communication scheme, such as OFDM, and can control the transmit power allocation of her signal among the channels. If Eve chooses to jam, she can control her jamming power allocation amongst the channels, but in this case cannot eavesdrop. In this paper we examine three different patterns for Alice's (and Eve's) behavior: (a) Alice assumes Eve employs either a pure jamming or eavesdropping strategy and determines her optimal mixed strategy under this assumption; (b) assuming a fixed probability with which Eve will jam/eavesdrop, Alice/Eve's equilibrium power allocation strategies can be determined, and then Eve chooses the probability that maximizes her payoff; (c) Eve chooses between two modes (either to jam or eavesdrop) as well as power allocations simultaneous with Alice's selection of power allocation. Using a game-theoretic formulation, the equilibrium strategies are found for each model and conditions where players apply mixed strategies are produced.

Dynamic spectrum access is a powerful approach to taking advantage of opportunities in spectrum to communicate. Access to these spectral opportunities should be regulated and monitored to prevent unapproved theft of spectral resources, which ultimately belong to a primary user. Unfortunately, most of the literature devoted to spectrum scanning does not consider the over-arching application that a spectrum thief might try to run. In this paper, we show that the thief's application (specifically, its QoS requirements), plays a critical role in how the thief should attempt to sneak spectrum and, consequently, a critical role in how the spectrum monitoring infrastructure should scan spectrum to detect thievery of spectral resources. We study the difference in the thief's behavior when considering bandwidth and delay as the two primary QoS parameters he is concerned with. Loosely speaking, this corresponds to sneaking for file-download versus streaming video, and the ultimate lesson learned is that the detection probability of unlicensed access to spectrum resources depends on the application type. As a consequence, knowledge of the application type allows for the primary user to improve spectrum scanning. Given the juxtaposition between the thief's and scanner's objectives, and the underlying dependency between detection and application QoS requirements, we finally formulate an adversarial Bayesian game where the scanner's scanning takes into account statistical knowledge about applications used by the user. The equilibrium strategies of this game are found in closed form what allowed to find their interesting properties. In particular, it was shown that the equilibrium sneaking strategies for different types of user are bandwidth-sharing, and we demonstrate how information about the application the user prefers to sneak at can improve the monitoring strategy.

We study revenue-maximizing in a wireless system where interested users share a common spectrum and interfere with each other. Capacity is increased in proportion of the number of users. Our objective is to design a scheme that achieves an optimal solution for the provider with respect to users strategy, bandwidth management and some fairness criteria. We consider a flat rate pricing for users. Two cases are studied: firstly, an approximation to the original problem when the provider has a perfect knowledge about the channel state of each user is proposed. In the second case, a decision theoretic approach based on a POMDP framework is elaborated when the provider has only a partial information on the system state. Additionally, we provide numerical results that illustrate the performance of the proposed solutions.

The problem of jamming plays an important role in ensuring the quality and security of wireless communications, especially at this moment when wireless networks are quickly becoming ubiquitous. Since jamming can be considered as a game in which jammer is playing against the user (transmitter) who would like to transmit signal with good quality and at the same time with a reasonable amount of energy, game theory is an appropriate tool for dealing with jamming. Here we investigate the effect of partially available information and correlation among sub-carriers on the user behavior. Specifically, to do so we deal with the scenario when the user does not know how jamming efforts are distributed among sub-carriers and the user does not know the fading channels' gains with certainty. As an object function for the user we consider SINR. We consider zero-sum games, so all of them can also be viewed as a minimax problem for the user playing against the nature. We study independent fading channel gains scenario as well as dependent fading channel gains scenario, both in discrete and continuous versions. We show that in all the scenarii the jammers equalize the quality of the best sub-carriers for the transmitter on as low level as their power constraints allow. Meanwhile the transmitter distributes his power among these jamming sub-carriers. We find the equilibrium strategies in closed form and specify the range of sub-carriers where the transmitter can expect the jamming attack. Also, we show for independent plot these strategies depend only on the expected value of the transmitters channel gains meanwhile for the dependent plot they depend on the whole spectra of these gains. Thus, for independent plot the behaviour of the jammer is less fine tuned under environment since it works with the expected gains. The user for both scenarios has to take the whole spectra of the jamming gains but, of course, for the independent scenario he is less specific because of the jammer.

We study power control in optimization and game frameworks. In the optimization framework there is a single decision maker who assigns network resources and in the game framework users share the network resources according to Nash equilibrium. The solution of these problems is based on so-called water-filling technique, which in turn uses bisection method for solution of non-linear equations for Lagrange multipliers. Here we provide a closed form solution to the water-filling problem, which allows us to solve it in a finite number of operations. Also, we produce a closed form solution for the Nash equilibrium in symmetric Gaussian interference game with an arbitrary number of users. Even though the game is symmetric, there is an intrinsic hierarchical structure induced by the quantity of the resources available to the users. We use this hierarchical structure to perform a successive reduction of the game. In addition to its mathematical beauty, the explicit solution allows one to study limiting cases when the crosstalk coefficient is either small or large. We provide an alternative simple proof of the convergence of the iterative water filling algorithm. Furthermore, it turns out that the convergence of Iterative water filling algorithm slows down when the crosstalk coefficient is large. Using the closed form solution, we can avoid this problem. Finally, we compare the non-cooperative approach with the cooperative approach and show that the non-cooperative approach results in a more fair resource distribution.