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Table Of Integrals Series And Products

Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Matrix Factorization Techniques for Recommender Systems

/pdf/a-break-in-the-clouds-towards-a-cloud-definition-svovsw1r5a.pdf

A Break in the Clouds: Towards a Cloud Definition

Unmanned aerial vehicle (UAV) communication has been deemed as a promising technology to collect data for the Internet of Things (IoT) in inaccessible areas. However, due to the limited UAV flight time, traditional UAV communication may not be competent for large-scale IoT data collection. This paper considers integrating non-orthogonal multiple access (NOMA) into UAV communication systems to collect data for large-scale IoT devices within UAV flight time. We aim to minimize the total energy consumption of IoT devices while ensuring data collection, by jointly optimizing UAV trajectory, IoT device scheduling and transmit power. The formulated problem is a mixed integer non-convex problem, which is challenging to solve in general. We propose a data collection optimization algorithm (DCOA) to solve it by applying the Generalized Benders Decomposition (GBD) and successive convex approximation (SCA) techniques. Then, a greedy algorithm (GA) is also proposed to reduce complexity by simplifying the optimization of UAV trajectory and IoT device scheduling. Finally, the numerical results demonstrate that, compared with traditional UAV communication systems, the NOMA-aided UAV system performs better in terms of data collection and lower total energy consumption of IoT devices can be achieved by DCOA.

/pdf/noma-aided-uav-data-collection-system-trajectory-45pgmo6qqi.pdf

NOMA-Aided UAV Data Collection System: Trajectory Optimization and Communication Design

Recently, mobile social cloud (MSC), formed by mobile users with social ties, has been advocated to allocate tasks of big data applications instead of relying the conventional cloud systems. However, due to the dynamic topology of networks and social features of users, how to optimally allocate tasks to mobile users based on the trust becomes a new challenge. Therefore, this paper proposes a novel incentive scheme based on the trust of mobile users in the MSC to allocate the tasks of big data. Firstly, a social trust degree is defined according to the social tie among users, the importance of task, and the available resources of networks. With the social trust degree, the task owner can select a group of mobile users as the candidates for task allocation. Secondly, a reverse auction game model is developed to study the interactions among the task owner and the candidates. With the reverse auction game model, the optimal strategy of task allocation can be obtained with a low cost for the task owner where the selected candidate of mobile users can also obtain the high profit. Finally, simulation experiments are carried out to prove that the proposal can outperform other existing methods with a low delay and a high efficiency to allocate tasks in the MSC.

Trust Based Incentive Scheme to Allocate Big Data Tasks with Mobile Social Cloud

Heterogeneous cloud radio access networks (H-CRANs), which take a separation of the remote radio units (RRHs) from the baseband units (BBUs), is considered to be a promising architecture for the future network due to its competitive advantages in both spectral efficiency and energy efficiency (EE). The RRH is mainly used to provide high data rate for mobile users (MTs) with high quality of service (QoS) requirements, while the evolved Node B (eNB) is deployed to guarantee the seamless coverage. To further enhance these benefits, in this paper, energy efficient uplink communications are investigated for H-CRANs with user cooperation and QoS guarantees. We formulate a joint optimization problem of relay selection, power allocation and network selection to maximize the EE of MTs with high QoS requirements. The optimization problem is a mixed-integer non-linear non-convex program and solved by Dinkelbach method and dual decomposition method. Moreover, a relay region selection algorithm is applied to reduce the computational complexity at the beginning of the optimization process. Numerical results show that the proposed scheme has improvement on the EE as compared with the scheme that joint power allocation and network selection and the scheme that joint relay selection and power allocation in H-CRANs.

Energy efficient resource allocation for heterogeneous cloud radio access networks with user cooperation and QoS guarantees

In heterogeneous wireless networks, rank aggregation based on multiple decision factors[1] has recently been proposed as a useful approach for network selection. For each decision factor, a rank of the candidate networks is derived according to the value of this decision factor. Then these decision factor dependent ranks are aggregated into a single rank and the top one is considered as a favorite network. However in the realistic scenario, the measurement on decision factor is often inaccurate so that the candidate networks are possibly not ranked appropriately. As a result, if there only exists the slight differences between the decision factor values of several candidate networks, same rank is preferable to these networks. The set of networks is therefore separated into several groups and these groups are ranked accordingly. Moreover the networks tied in the same group have the same rank. In this paper, a new approach namely median based network selection method is therefore proposed to handle such partial tied rank aggregation problem.

https://www.ece.uvic.ca/~zhengl/materials/WCNC09WZYS.pdf

Median Based Network Selection in Heterogeneous Wireless Networks

Aiming at large-scale job scheduling, allocating resource dynamically in order to reduce cost is a significant problem in cloud. In this paper, we study the resource allocation at the application level, instead of studying to map the physical resources to virtual resources for better resource utilization in cloud computing environment. We propose a multi-dimensional resource allocation scheme for cloud computing that dynamically allocates the virtual resources among the cloud computing applications to reduce cost by using fewer nodes to process applications. In our model we adopt a two-stage algorithm to solve this multi-constraint integer programming problem. Experiment results show the proposed scheme can improve resource utilization and reduce cost of data center.

Ying Wang

Papers

NOMA-Aided UAV Data Collection System: Trajectory Optimization and Communication Design

Trust Based Incentive Scheme to Allocate Big Data Tasks with Mobile Social Cloud

Energy efficient resource allocation for heterogeneous cloud radio access networks with user cooperation and QoS guarantees

Median Based Network Selection in Heterogeneous Wireless Networks

A Multi-dimensional Resource Allocation Algorithm in Cloud Computing ⋆