The MIMO Iterative Waterfilling Algorithm

The concept of cognitive radio (CR) has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. In this paper we propose and analyze a totally decentralized approach, based on game theory, to design cognitive MIMO transceivers, who compete with each other to maximize their information rate. The formulation incorporates constraints on the transmit power as well as null and/or soft shaping constraints on the transmit covariance matrix, so that the interference generated by secondary users be confined within the temperature-interference limit required by the primary users. We provide a unified set of conditions that guarantee the uniqueness and global asymptotic stability of the Nash equilibrium of all the proposed games through totally distributed and asynchronous algorithms. Interestingly, the proposed algorithms overcome the main drawback of classical waterfilling based algorithms-the violation of the temperature-interference limit-and they have the desired features required for CR applications, such as low-complexity, distributed implementation, robustness against missing or outdated updates of the users, and fast convergence behavior.

This paper presents a pragmatic example of how to use Ada tasks with Add machines such as SuperMicro(TM) for scientific computing. First, a class of asynchronous concurrent Newton's algorithms: Purely-Asynchronous (PAN), Asynchronous (AN), and Semi-Asynchronous (SAN) algorithms are introduced for distributed computing environment. A sufficient condition is shown to guarantee local convergence of these asynchronous algorithms. Moreover, it is proved that the PAN algorithm is linearly convergent, the AN algorithm is super-linearly convergent, and the SAN algorithm is quadratically convergent. The order of convergence depends on the degree of interaction among computing modules. Second, a non-deterministic program for the asynchronous algorithm is provided by using Ada tasks. The asynchronous algorithm/program is superior to the synchronized counterpart with respect to computation speed and reliability. Lastly, this paper describes a way where the asynchronous algorithm/program can be realized as a hierarchic distributed system with Ada machines. A preliminary result is shown with MicroAda/SuperMicro(TM).

Post-quantum cryptography is essential for securing digital communications against threats posed by quantum computers. Researchers have focused on developing algorithms that can withstand attacks from both classical and quantum computers, thereby ensuring the security of data transmissions over public networks. A critical component of this security is the key agreement protocol, which allows two parties to establish a shared secret key over an insecure channel. This paper introduces two novel post-quantum key agreement protocols that can be easily implemented on standard computers using rectangular or rank-deficient matrices, exploiting the generalizations of the matrix power function, which is a generator of NP-hard problems. We provide basic concepts and proofs, pseudocodes, and examples, along with a discussion of complexity.

Discovering theorems in game theory: Two-person games with unique pure Nash equilibrium payoffs

The Keynesian beauty contest revisited

Traditional mobile crowdsensing has shown a great potential to address large-scale data sensing problems by allocating sensing tasks to pervasive mobile users with smart devices. As crowdsensing service provider involves data collection from mobile users, the issue of providing rewards to incentivize mobile users is fundamentally important to ensure the sustainability of crowdsensing system. Recently, socially-aware crowdsensing services have been introduced as the integration of social networks and crowdsensing platforms. For example, in health-related crowdsensing applications, a mobile user benefits from information regarding food, exercise, medicine and medical treatment collected and shared by her socially-connected friends and family members. In this thesis, incentive mechanism design is revisited in the context of socially-aware crowdsensing, where the game theory tool is used to study the interactions between crowdsensing service provider and mobile users. In the first part of the thesis, incentive mechanism is designed by considering the underlying social network effects amid mobile social networks, for motivating the participants. Namely, one MU will obtain additional benefits from information contributed or shared by local neighbors in social networks. The process of rewarding and participating is modeled as a two-stage game, and backward induction is used to analyze the mobile users' participation level and the crowdsensing service provider's optimal reward mechanism. The analytical expressions are derived for the discriminatory incentive as well as the uniform incentive mechanisms. In the second part of the thesis, information asymmetry challenges are investigated. A Bayesian Stackelberg game with incomplete information is formulated to analyze the interaction between the crowdsensing service provider and mobile users, where the social structure information, i.e., the social network effects, among mobile users is uncertain. The existence and uniqueness of the Bayesian Stackelberg equilibrium is analytically validated by identifying the best response strategies of the mobile users. To be more general and practical, different with the former two parts, incentive mechanism in presence of multiple crowdsensing service providers is studied in the third part of the thesis. Understanding the behaviors of mobile users and service providers in socially-aware crowdsensing is of paramount importance for incentive mechanisms. With this focus, a multi-leader and multi-follower Stackelberg game approach is proposed to model the strategic interactions among service providers and mobile users, where the social influence of mobile users and the strategic interconnections of service providers are jointly and formally integrated into the game modeling. Through backward induction methods, the existence and uniqueness of the Stackelberg equilibrium are theoretically proved. In summary, this thesis addresses a few urgent challenging problems with the tools of game theory in the real implementation of incentive mechanism design in the context of socially-aware crowdsensing. Extensive numerical simulations are also conducted to illustrate some important properties of the equilibrium. Finally, several promising research directions are outlined for the future work.

Game theory based on the theory and thought of classical math has brought far-reaching affects in the field of economics, sociology, and so on. However, classical game theory can find no way out when game circumstance faces to uncertainty condition, such as finite logos, finite knowledge, small sample, and inadequate information, the payoff value of game can only be described with grey number. So study on grey matrix game has the most important theoretic value and actualistic meaning. How to solve the grey matrix game with high efficiency is the key problem which must be solved in the theory research and application of this field. Matrix solution method of grey matrix game is simple and effective. This paper has defined grey full rank payoff value expansion square matrix of grey matrix game, and has also proved that besides the value of grey element at the right and bottom edge of inverse matrix of grey full rank expansion square matrix, the value of grey element at its last line and right column is corresponding the optimal grey game strategies of player 1 and 2 separately.

A joint power and rate control using game theory algorithm is proposed in heterogeneous networks environment with interference among different systems. It designs a novel revenue function based on the fairness of users' power control and the rate allocation, accompanying with the interference of the primary users caused by different users. The existence and uniqueness of the Nash equilibrium of game theory are derived by rigorous mathematical. Furthermore, simulation results show that the proposed algorithm can improve users' power control and rate allocation significantly.

In the resource constraint Wireless Sensor Network(WSN), link quality and node residual energy are the key factors that need to be considered in the routing problem. This paper proposes a routing algorithm based on game theory. Firs it sets up the game model based on the Quality of Service(QoS) and node residual energy. Then it shows that the game has a unique Nash equilibrium solution, and analyses the feasibility of the algorithm. The simulation results show that the proposed model could optimize the QoS, reduce the energy consumption of nodes and prolong the network life time.

Unmanned aerial vehicles (UAVs) can be utilized as airborne base stations to deliver wireless communication and federated learning (FL) training services for ground vehicles. However, most existing studies assume that vehicles (clients) and UAVs (model owners) offer services voluntarily. In reality, participants (FL clients and model owners) are selfish and will not engage in training without compensation. Meanwhile, due to the heterogeneity of participants and the presence of free-riders and Byzantine behaviors, the quality of vehicles’ model updates can vary significantly. To incentivize participants to engage in model training and ensure reliable outcomes, this paper designs a reliable incentive mechanism (FedBeam) based on game theory. Specifically, we model the cooperation problem between model owners and clients as a two-layer Stackelberg game and prove the existence and uniqueness of the Stackelberg equilibrium (SE). For the cooperation among model owners, we formulate the problem as a coalition game and based on this, analyze and design a coalition formation algorithm to derive the Pareto optimal social utility. Additionally, to achieve reliable FL model updates, we design a weighted-beta (Wbeta) reputation update mechanism to incentivize FL clients to provide high-quality model updates. The experimental results show that compared to the baselines, the proposed incentive mechanism improves social welfare by 17.6% and test accuracy by 5.5% on simulated and real datasets, respectively.

In this paper, a joint power and subcarrier allocation scheme in single-cell uplink OFDMA systems is proposed based on game theory. Our goal is to maximize the power efficiency of each user under peak power constraint. For the purpose, a utility function is designed which can enhance the rate per joule of energy consumed greatly, and the existence and uniqueness of the Nash equilibrium of the function is proved. To bring Pareto improvement, and to overcome the far-near effect, the pricing scheme is introduced. The simulation results show that the power efficiency of the proposed algorithm increases greatly over that of the MaxRt+WF (maximal marginal rate subcarrier and waterfilling power allocation) and MaxFA+WF (fixed subcarrier allocation and waterfilling power allocation).

The growing popularity of Internet of Things (IoT) with the requirements of highly reliable and low latency has imposed huge challenges to current cellular networks. Using small aerial platforms like unmanned aerial vehicles (UAVs) to assist terrestrial base stations (BSs) is attractive, but it often challenged by the lack of UAV access selection and resource allocation algorithm to balance the network performance and service cost. In this paper, we study the UAV access selection and BS bandwidth allocation problems in a UAV assisted IoT communication network, where a hierarchical game framework is presented. The complicated interactions among UAVs and BSs as well as the cyclic dependency is studied by applying the Stackelberg game theory. Wherein, the access competition among groups of UAVs is formulated as a dynamic evolutionary game and solved by an evolutionary equilibrium. On the other hand, the problem of how much bandwidth should BSs allocate to the UAVs is modeled as a noncooperative game, where the existence and the uniqueness of Nash equilibrium is analyzed. Stochastic geometry tool is used to model the position distribution of network nodes and drive the payoff expressions by taking into account different network parameters. The analytical results for the proposed hierarchical game model and the corresponding solutions are evaluated via simulations, which verify both the validity of our analysis and the effectiveness of the proposed algorithms.

Cognitive radio (CR) has achieved increasing attention to improve the spectrum utilisation by allowing the coexistence of primary users (PUs) and cognitive users (CUs) in the same frequency band. As the spectrum of interest is licenced to primary network, power control must be carried out within the CR system so that no excessive interference is caused to PUs. In this study, the problem of power control is investigated in CR systems based on game theory subject to interference power constraint at PU and the signal‐to‐interference‐plus‐noise ratio (SINR) constraint of each CU. The objective is to reduce the power consumption caused by some CUs’ SINR over the target value. First, a non‐cooperation power control game is formulated, and then an adaptive power control algorithm based on feedback function is proposed. Moreover, the existence and uniqueness of Nash equilibrium are proved. Simulation results show that, compared with other distributed algorithms, the proposed algorithm can reduce the power consumption and overcome the near‐far effect.

Power control plays an important role in reducing interference and conflict between Wireless Body Area Networks (WBAN). The goal of power control is to send the collected data with as small and appropriate transmission power as possible, which largely depends on the network type or different application scenarios. In this paper, a utility function based on network connectivity is established based on the basic principle of non-cooperative game theory. The algorithm considers the cost function based on SINR and proves the existence and uniqueness of Nash equilibrium solution.The algorithm proves that the Nash equilibrium solution exists and is unique through the analysis of the utility function.

This paper deals with the numerical solution of financial applications, more specifically the computation of American and European options derivatives modeled by boundary value problems. In such applications we have to solve large-scale algebraic linear systems. We concentrate on synchronous and asynchronous parallel iterative algorithms carried out on Grid’5000, by using an experimental peer-to-peer platform. The properties of the operators arising in the discretized problem ensure the convergence of the parallel iterative synchronous and asynchronous algorithms. Different detection convergence algorithms are tested for asynchronous iterations. Computational experiments performed on distributed architectures are presented and analyzed.