With the increasing connectivity enabled by the Internet of Things (IoT), security becomes a critical concern, and users should invest to secure their IoT applications. Due to the massive devices in the IoT network, users cannot be aware of the security policies taken by all its connected neighbors. Instead, a user makes security decisions based on the cyber risks that he perceives by observing a selected number of nodes. To this end, we propose a model which incorporates the limited attention or bounded rationality nature of players in the IoT. Specifically, each individual builds a sparse cognitive network of nodes to respond to. Based on this simplified cognitive network representation, each user then determines his security management policy by minimizing his own real-world security cost. The bounded rational decision-makings of players and their cognitive network formations are interdependent and thus should be addressed in a holistic manner. We establish a games-in-games framework and propose a Gestalt Nash equilibrium (GNE) solution concept to characterize the decisions of agents and quantify their risk of bounded perception due to the limited attention. In addition, we design a proximal-based iterative algorithm to compute the GNE. With case studies of smart communities, the designed algorithm can successfully identify the critical users whose decisions need to be taken into account by the other users during the security management.
Humans with limited knowledge or cognitive resources are bounded rational, since they cannot pay attention to all the information @cite_36 @cite_19 . Gabaix has proposed a sparse max'' operator to model the limited attention of players in which each agent builds a simplified model of the network based on an @math norm @cite_13 . Built upon @cite_5 which includes some preliminary results, our work leverages on the established sparse max'' operator and formulates a constrained game program to capture the bounded cognition ability of players in the IoT. In addition, we further consider the risk management of each user based on their underperceived cyber risks over the network.
@cite_36 @cite_19 @cite_5 @cite_13
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With the increasing connectivity enabled by the Internet of Things (IoT), security becomes a critical concern, and users should invest to secure their IoT applications. Due to the massive devices in the IoT network, users cannot be aware of the security policies taken by all its connected neighbors. Instead, a user makes security decisions based on the cyber risks that he perceives by observing a selected number of nodes. To this end, we propose a model which incorporates the limited attention or bounded rationality nature of players in the IoT. Specifically, each individual builds a sparse cognitive network of nodes to respond to. Based on this simplified cognitive network representation, each user then determines his security management policy by minimizing his own real-world security cost. The bounded rational decision-makings of players and their cognitive network formations are interdependent and thus should be addressed in a holistic manner. We establish a games-in-games framework and propose a Gestalt Nash equilibrium (GNE) solution concept to characterize the decisions of agents and quantify their risk of bounded perception due to the limited attention. In addition, we design a proximal-based iterative algorithm to compute the GNE. With case studies of smart communities, the designed algorithm can successfully identify the critical users whose decisions need to be taken into account by the other users during the security management. With the increasing connectivity enabled by the Internet of Things (IoT), security becomes a critical concern, and the users should invest to secure their IoT applications. Due to the massive devices in the IoT network, users cannot be aware of the security policies taken by all its connected neighbors. Instead, a user makes security decisions based on the cyber risks he perceives by observing a selected number of nodes. To this end, we propose a model which incorporates the limited attention or bounded rationality nature of players in the IoT. Specifically, each individual builds a sparse cognitive network which includes the users to respond to. Based on this simplified cognitive network representation, each user then determines his security investment policy by minimizing his own real-world security cost. The bounded rational decision-makings of players and their cognitive network formations are interdependent, and thus should be addressed in a holistic manner. We propose a Gestalt Nash equilibrium (GNE) solution concept to characterize the decisions of agents. Then, we design a proximal-based iterative algorithm to compute the GNE and show its convergence. With case studies to smart home communities, the designed algorithm can successfully identify the critical users whose decisions need to be taken into account by the other users during the security investment. This paper considers a sparse signal recovery task in time-varying (time-adaptive) environments. The contribution of the paper to sparsity-aware online learning is threefold; first, a generalized thresholding (GT) operator, which relates to both convex and non-convex penalty functions, is introduced. This operator embodies, in a unified way, the majority of well-known thresholding rules which promote sparsity. Second, a non-convexly constrained, sparsity-promoting, online learning scheme, namely the adaptive projection-based generalized thresholding (APGT), is developed that incorporates the GT operator with a computational complexity that scales linearly to the number of unknowns. Third, the novel family of partially quasi-nonexpansive mappings is introduced as a functional analytic tool for treating the GT operator. By building upon the rich fixed point theory, the previous class of mappings establishes also a link between the GT operator and a union of linear subspaces; a non-convex object which lies at the heart of any sparsity promoting technique, batch or online. Based on this functional analytic framework, a convergence analysis of the APGT is provided. Extensive experiments suggest that the APGT exhibits competitive performance when compared to computationally more demanding alternatives, such as the sparsity-promoting affine projection algorithm (APA)- and recursive least-squares (RLS)-based techniques. This paper considers the design of efficient strategies that allow cognitive users to choose frequency bands to sense and access among multiple bands with unknown parameters. First, the scenario in which a single cognitive user wishes to opportunistically exploit the availability of frequency bands is considered. By adopting tools from the classical bandit problem, optimal as well as low complexity asymptotically optimal solutions are developed. Next, the multiple cognitive user scenario is considered. The situation in which the availability probability of each channel is known is first considered. An optimal symmetric strategy that maximizes the total throughput of the cognitive users is developed. To avoid the possible selfish behavior of the cognitive users, a game-theoretic model is then developed. The performance of both models is characterized analytically. Then, the situation in which the availability probability of each channel is unknown a priori is considered. Low-complexity medium access protocols, which strike an optimal balance between exploration and exploitation in such competitive environments, are developed. The operating points of these low-complexity protocols are shown to converge to those of the scenario in which the availability probabilities are known. Finally, numerical results are provided to illustrate the impact of sensing errors and other practical considerations. This paper defines and analyzes a "sparse max" operator, which is a less than fully attentive and rational version of the traditional max operator. The agent builds (as economists do) a simplified model of the world which is sparse, considering only the variables of first-order importance. His stylized model and his resulting choices both derive from constrained optimization. Still, the sparse max remains tractable to compute. Moreover, the induced outcomes reflect basic psychological forces governing limited attention. The sparse max yields a behavioral version of two basic chapters of the microeconomics textbook: consumer demand and competitive equilibrium. We obtain a behavioral version of Marshallian and Hicksian demand, the Slutsky matrix, the Edgeworth box, Roy's identity etc. The Slutsky matrix is no longer symmetric: non-salient prices are associated with anomalously small demand elasticities. Because the consumer exhibits nominal illusion, in the Edgeworth box, the offer curve is a two-dimensional surface rather than a one-dimensional curve. As a result, different aggregate price levels correspond to materially distinct competitive equilibria, in a similar spirit to a Phillips curve. This framework provides a way to assess which parts of basic microeconomics are robust, and which are not, to the assumption of perfect maximization. We propose a probabilistic model based on stochastic geometry to analyze cognitive radio in a large wireless network with randomly located users sharing the medium with carrier sensing multiple access. Analytical results are derived on the impact of the interaction between primary and secondary users, on their medium access probability, coverage probability and throughput. These results can be seen as the continuation of the theory of priorities in queueing theory to spatial processes. They give insight into the guarantees that can be offered to primary users and more generally on the possibilities offered by cognitive radio to improve the effectiveness of spectrum utilization in such networks. We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion. We investigate the problem of reconstructing a high-dimensional nonnegative sparse vector from lower-dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes can be more efficient both with respect to signal sensing as well as reconstruction complexity. Known constructions use the adjacency matrices of expander graphs, which often lead to recovery algorithms which are much more efficient than minimization. However, prior constructions of sparse measurement matrices rely on expander graphs with very high expansion coefficients which make the construction of such graphs difficult and the size of the recoverable sets very small. In this paper, we introduce sparse measurement matrices for the recovery of nonnegative vectors, using perturbations of the adjacency matrices of expander graphs requiring much smaller expansion coefficients, hereby referred to as minimal expanders. We show that when minimization is used as the reconstruction method, these constructions allow the recovery of signals that are almost three orders of magnitude larger compared to the existing theoretical results for sparse measurement matrices. We provide for the first time tight upper bounds for the so called weak and strong recovery thresholds when minimization is used. We further show that the success of optimization is equivalent to the existence of a “unique” vector in the set of solutions to the linear equations, which enables alternative algorithms for minimization. We further show that the defined minimal expansion property is necessary for all measurement matrices for compressive sensing, (even when the non-negativity assumption is removed) therefore implying that our construction is tight. We finally present a novel recovery algorithm that exploits expansion and is much more computationally efficient compared to minimization. Given a dictionary that consists of multiple blocks and a signal that lives in the range space of only a few blocks, we study the problem of finding a block-sparse representation of the signal, i.e., a representation that uses the minimum number of blocks. Motivated by signal image processing and computer vision applications, such as face recognition, we consider the block-sparse recovery problem in the case where the number of atoms in each block is arbitrary, possibly much larger than the dimension of the underlying subspace. To find a block-sparse representation of a signal, we propose two classes of nonconvex optimization programs, which aim to minimize the number of nonzero coefficient blocks and the number of nonzero reconstructed vectors from the blocks, respectively. Since both classes of problems are NP-hard, we propose convex relaxations and derive conditions under which each class of the convex programs is equivalent to the original nonconvex formulation. Our conditions depend on the notions of mutual and cumulative subspace coherence of a dictionary, which are natural generalizations of existing notions of mutual and cumulative coherence. We evaluate the performance of the proposed convex programs through simulations as well as real experiments on face recognition. We show that treating the face recognition problem as a block-sparse recovery problem improves the state-of-the-art results by 10 with only 25 of the training data. Cognitive small cell networks have been envisioned as a promising technique for meeting the exponentially increasing mobile traffic demand. Recently, many technological issues pertaining to cognitive small cell networks have been studied, including resource allocation and interference mitigation, but most studies assume non-cooperative schemes or perfect channel state information (CSI). Different from the existing works, we investigate the joint uplink subchannel and power allocation problem in cognitive small cells using cooperative Nash bargaining game theory, where the cross-tier interference mitigation, minimum outage probability requirement, imperfect CSI and fairness in terms of minimum rate requirement are considered. A unified analytical framework is proposed for the optimization problem, where the near optimal cooperative bargaining resource allocation strategy is derived based on Lagrangian dual decomposition by introducing time-sharing variables and recalling the Lambert-W function. The existence, uniqueness, and fairness of the solution to this game model are proved. A cooperative Nash bargaining resource allocation algorithm is developed, and is shown to converge to a Pareto-optimal equilibrium for the cooperative game. Simulation results are provided to verify the effectiveness of the proposed cooperative game algorithm for efficient and fair resource allocation in cognitive small cell networks. This paper studies the problem of recovering a sparse signal x ∈ ℝn from highly corrupted linear measurements y = Ax + e ∈ ℝm, where e is an unknown error vector whose nonzero entries may be unbounded. Motivated by an observation from face recognition in computer vision, this paper proves that for highly correlated (and possibly overcomplete) dictionaries A, any sufficiently sparse signal x can be recovered by solving an l1 -minimization problem min ||x||1 + ||e||1 subject to y = Ax + e. More precisely, if the fraction of the support of the error e is bounded away from one and the support of a: is a very small fraction of the dimension m, then as m becomes large the above l1 -minimization succeeds for all signals x and almost all sign-and-support patterns of e. This result suggests that accurate recovery of sparse signals is possible and computationally feasible even with nearly 100 of the observations corrupted. The proof relies on a careful characterization of the faces of a convex polytope spanned together by the standard crosspolytope and a set of independent identically distributed (i.i.d.) Gaussian vectors with nonzero mean and small variance, dubbed the "cross-and-bouquet" (CAB) model. Simulations and experiments corroborate the findings, and suggest extensions to the result. Mobile networks are increasingly becoming capacity limited such that more base stations and smaller cells or more spectrum are required to serve the subscribers' increasing data usage. Among several challenges, the establishment of new base station sites becomes challenging and expensive. This study proposes and analyzes critical aspects of a business case where a mobile operator offloads its mobile LTE network by deploying cognitive femtocells. When aided by a sensor network the cognitive femtocell will be able to use frequencies other than the mobile network and hence increase its power to cover outdoor areas and neighbour buildings. This cognitive femtocell strategy will be compared with an alternative strategy where an operator deploys conventional femtocells and has to build additional base stations to meet the traffic demands. The business case analysis illustrates that there is a potential for cost savings when offloading the mobile network with cognitive femtocells when compared to the alternative strategy. It must be emphasized that the studied concept is innovative and that the business case period starts in 2017, hence, parameter assumptions are uncertain. Therefore, as the most important message of this work, sensitivity analysis is used to reveal the most critical aspects of the cognitive femtocell business case. It is found that the most critical parameters regarding the cognitive femtocell are the price for backhauling, the number of users supported and the coverage. Furthermore, an optimal coverage radius for the cognitive femtocell for lowest possible costs is found. Costs related to the fixed sensor network are found to be less critical since sensors are embedded in the cognitive femtocells. Sensitivity analysis is also presented for spectral efficiency, cognitive and conventional femtocell offloading gain, sensor density and price, customer density and price for base station site establishment. This paper studies the coverage problem in an unknown environment by a Mobile Sensor Network (MSN). Each agent in the MSN has sensing, communication, computation and moving capabilities to complete sensing tasks. Here the agents need to relocate themselves, from their initial random locations, to their optimal configuration. The proposed algorithm is based on game theory control where a collection of distributed agents use their local information to make decisions. A state-based potential game is defined in which each agent's utility function is designed to consider the trade off between the worth of the covered area and the energy consumption. The agents employ binary log-linear learning to update their actions in each iteration in order to converge to the Nash equilibrium. As the agents do not have the knowledge of the sensing area, a Maximum Likelihood estimation scheme is used to estimate the unknown parameters of a Gaussian Mixture Model (GMM). Then in order to feed the estimation algorithm with more informative data, a mutual information term is added to the agents' utility functions. The mutual information is utilized to determine which observation can improve the agent's knowledge of the unobserved area more. Simulation results are provided to verify the performance of the proposed algorithm. Thanks to the rapid development of information technology, the size of a wireless network is becoming larger and larger, which makes spectrum resources more precious than ever before. To improve the efficiency of spectrum utilization, game theory has been applied to study efficient spectrum sharing for a long time. However, the scale of wireless networks in existing studies is relatively small. In this paper, we introduce a novel game called aggregative game and use it to model spectrum sharing in large-scale, heterogeneous, and dynamic networks. Meanwhile, the massive usage of the spectrum leads to easier divulgence of privacy of spectrum users, which calls for privacy and truthfulness guarantees. In a large decentralized scenario, each user has no priori about other users’ channel access decisions, which forms an incomplete information game. A “weak mediator,” e.g., the base station or licensed spectrum regulator, is introduced and it turns the incomplete spectrum sharing game into a complete one. This is essential in reaching a Nash equilibrium (NE). By utilizing past channel access experience, we propose an online learning algorithm to improve the utility of each user. We show that the learning algorithm achieves an NE over time and provides no regret guarantee for each user. Specifically, our mechanism admits an approximate ex-post NE, and is joint differentially private and incentive-compatible. Efficiency of the approximate NE is evaluated, and innovative scaling law results are disclosed. We also provide simulation results to verify our analysis. Imitating successful behavior is a natural and frequently applied approach when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic congestion games. We propose to study concurrent imitation dynamics that emerge when each player samples another player and possibly imitates this agents' strategy if the anticipated latency gain is sufficiently large. Our main focus is on convergence properties. Using a potential function argument, we show that these dynamics converge in a monotonic fashion to stable states. In such a state none of the players can improve their latency by imitating others. As our main result, we show rapid convergence to approximate equilibria. At an approximate equilibrium only a small fraction of agents sustains a latency significantly above or below average. In particular, imitation dynamics behave like fully polynomial time approximation schemes (FPTAS). Fixing all other parameters, the convergence time depends only in a logarithmic fashion on the number of agents. Since imitation processes are not innovative they cannot discover unused strategies. Furthermore, strategies may become extinct with non-zero probability. For the case of singleton games, we show that the probability of this event occurring is negligible. Additionally, we prove that the social cost of a stable state reached by our dynamics is not much worse than an optimal state in singleton congestion games with linear latency functions. While we concentrate on the case of symmetric network congestion games, most of our results do not explicitly use the network structure. They continue to hold accordingly for general symmetric and asymmetric congestion games when each player samples within his commodity. We revisit in this paper the resilience problem of routing traffic in a parallel link network model with a malicious player using a game theoretic framework. Consider that there are two players in the network: the first player wishes to split its traffic so as to minimize its average delay, which the second player, i.e., the malicious player, tries to maximize. The first player has a demand constraint on the total traffic it routes. The second player controls the link capacities: it can decrease by some amount the capacity of each link under a constraint on the sum of capacity degradation. We first show that the average delay function is convex both in traffic and in capacity degradation over the parallel links and thus does not have a saddle point. We identify best responses strategies of each player and compute both the max-min and the min-max values of the game. We are especially interested in the min max strategy as it guarantees the best performance under worst possible link capacity degradation. It thus allows to obtain routing strategies that are resilient and robust. We compare the results of the min-max to those obtained under the max-min strategies. We provide stable algorithms for computing both max-min and min-max strategies as well as for best responses. In this work we derive fundamental limits for many linear and non-linear sparse signal processing models including group testing, quantized compressive sensing, multivariate regression and observations with missing features. In general, sparse signal processing problems can be characterized in terms of the following Markovian property. We are given a set of N variables X1, X2, ..., XN, and there is an unknown subset of variables S ⊂ 1, 2, ..., N that are relevant for predicting outcomes outputs Y. In other words, when Y is conditioned on Xn nϵS it is conditionally independent of the other variables, Xn n∉S. Our goal is to identify the set S from samples of the variables X and the associated outcomes Y. We characterize this problem as a version of the noisy channel coding problem. Using asymptotic information theoretic analyses, we establish mutual information formulas that provide sufficient and necessary conditions on the number of samples required to successfully recover the salient variables. These mutual information expressions unify conditions for both linear and non-linear observations. We then compute sample complexity bounds for the aforementioned models, based on the mutual information expressions. Motivated in part by the “rational inattention” framework of information-constrained decision-making by economic agents, we have recently introduced a general model for average-cost optimal control of Markov processes subject to mutual information constraints [1]. The optimal information-constrained control problem reduces to an infinite-dimensional convex program and admits a decomposition based on the Bellman error, which is the object of study in approximate dynamic programming. In this paper, we apply our general theory to an information-constrained variant of the scalar linear-quadratic-Gaussian (LQG) control problem. We give an upper bound on the optimal steady-state value of the quadratic performance objective and present explicit constructions of controllers that achieve this bound. We show that the obvious certainty-equivalent control policy is suboptimal when the information constraints are very severe, and exhibit another policy that performs better in this low-information regime. In the two extreme cases of no information (open-loop) and perfect information, these two policies coincide with the optimum. Participatory sensing is becoming more popular with the help of sensor-embedded smartphones to retrieve context-aware information for users. However, new challenges arise for the maintenance of the energy supply, the support of the quality-of-information (QoI) requirements, and the generation of maximum revenue for network operator, but with sparsely research exposure. This paper proposes a novel efficient network management framework to tackle the above challenges, where four key design elements are introduced. First is the QoI satisfaction index, where the QoI benefit the queries receive is quantified in relation to the level they require. Second is the credit satisfaction index, where the credits are used by the network operator to motivate the user participation, and this index is to quantify its degree of satisfaction. Third is the Gur Game-based distributed energy control, where the above two indexes are used as inputs to the mathematical framework of the Gur Game for distributed decision-making. Fourth is the dynamic pricing scheme, based on a constrained optimization problem to allocate credits to the participants while minimizing the necessary adaptation of the pricing scheme from the network operator. We finally evaluate the proposed scheme under an event occurrence detection scenario, where the proposed scheme successfully guarantees less than 7 detection outage, saves 80 of the energy reserve if compared with the lower bound solution, and achieves the suboptimum with only 4 gap if compared with optimal solution. In a complex and uncertain world, humans and animals make decisions under the constraints of limited knowledge, resources, and time. Yet models of rational decision making in economics, cognitive science, biology, and other fields largely ignore these real constraints and instead assume agents with perfect information and unlimited time. About forty years ago, Herbert Simon challenged this view with his notion of "bounded rationality." Today, bounded rationality has become a fashionable term used for disparate views of reasoning. This book promotes bounded rationality as the key to understanding how real people make decisions. Using the concept of an "adaptive toolbox," a repertoire of fast and frugal rules for decision making under uncertainty, it attempts to impose more order and coherence on the idea of bounded rationality. The contributors view bounded rationality neither as optimization under constraints nor as the study of people's reasoning fallacies. The strategies in the adaptive toolbox dispense with optimization and, for the most part, with calculations of probabilities and utilities. The book extends the concept of bounded rationality from cognitive tools to emotions; it analyzes social norms, imitation, and other cultural tools as rational strategies; and it shows how smart heuristics can exploit the structure of environments.