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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

This paper addresses the filter-design issues for multi-user non-regenerative MIMO-relay systems. Based on the perfect channel state information (CSI), optimal joint linear filter schemes at the base station and the relay are derived, aiming to minimize the mean squared error (MSE). We first propose the joint optimal filter scheme in the downlink scenario along with a more practical suboptimal scheme, and then a closed-form optimal solution in the uplink scenario is exploited. Numerical results show that the proposed joint schemes can reduce the bit error rate (BER) significantly, especially for the high SNR case.

Joint Linear Filter Design in Multi-User Non-Regenerative MIMO-Relay Systems

Device-to-device (D2D) communication with increased spectral efficiency and reduced communication delay has undoubtedly become a general trend in future wireless networks. However, when D2D communication is incorporated into small cell networks (SCNs) with large number of randomly overlapped small cells, the co-channel interference between small cell users (SUEs) and D2D users is an inevitable challenge, especially with the heterogeneous spectrum, i.e., licensed spectrum bands and unlicensed spectrum bands. In this paper, we study the downlink channel allocation in D2D-assisted small cell networks with heterogeneous spectrum bands. By taking the required data rate of users and the interference constraint of SUEs into account, we formulate a channel allocation problem integrating channel selection and channel sharing to maximize the network utility, which is the service satisfaction of all users. To derive the solution, we decompose the optimization problem into two games: a potential game and a coalition game. Then, a potential game-based scheme using an interference graph and a coalition scheme with D2D user transferring is proposed to solve these two games, respectively. Based on these schemes, a two-stage distributed channel allocation algorithm is proposed and can converge with low computational complexity. Moreover, the simulation results reveal that the proposed algorithm could achieve high system throughput and network utility.

/pdf/distributed-resource-allocation-for-d2d-assisted-small-cell-3o7rtbdxch.pdf

Distributed Resource Allocation for D2D-Assisted Small Cell Networks With Heterogeneous Spectrum

Emerging mobile cloud computing (MCC) technology offers great potential for the mobile terminals to support running highly sophisticated applications. However, supporting such applications needs efficient resource management from cloud servers and mobile terminals. Moreover, the resource management technologies based on quality of experiences (QoE) can meet the demand of end users in a better way than those based on quality of services. In this paper, we address the resource management problem of MCC network with an acceptable QoE. Based on multi-leader multi-follower two-stage Stackelberg game model, the proposed scheme maximizes the utility function of MCC networks. Considering the scenario in which the cloud servers and mobile terminals are selfish to maximize their own interests, the network performance is greatly affected by their greediness. To achieve better network performance, control decisions are coupled with one another. Utility function considers not only the spectral efficiency and user satisfaction in the mobile terminal but also the pricing information in the cloud. Our proposed scheme can obtain a well-balanced performance between mobile terminals and cloud servers. In addition, the existence of Nash equilibrium in the proposed scheme is investigated. Theoretically, the maximum and minimum selling prices of bandwidth are deduced. Simulation results show that the effectiveness of the proposed algorithm and our proposed scheme outperforms equal allocation scheme in terms of the user satisfaction and network revenue.

Multi-leader Multi-follower Stackelberg Game Based Dynamic Resource Allocation for Mobile Cloud Computing Environment

Proactive caching at the mobile network edge has been considered as a promising technology for enhancing users' Quality of Experience (QoE) and reducing redundant transmissions over the already overburdened cellular networks. The problem of video file caching in wireless Device-to-Device (D2D) communication networks, in which mobile users designated as helper users store popular video files and serve other requesting users via D2D localized transmissions, is studied in this paper. As personalized video recommendation systems are widely applied in video sites such as YouTube and Netflix, they cause mobile users' diversification and individuation in file preferences and users may make selfish caching decisions. Moreover, designing the file placement in caches is a task of hugely computational complexity due to the vast number of involved files and users. In this paper, we simultaneously cluster users and files into different interest groups and then propose a greedy intra-cluster caching scheme to greatly reduce its complexity. And we also compare the performance of each clustering algorithm while the file preferences matrix becomes high dimensional, sparse and highly asymmetric. Simulation results confirm that, with markedly reduced complexity, our proposed greedy caching scheme with spectral clustering using cosine similarity as the distance measure achieves near-optimal delay performance.

Clustered device-to-device caching based on file preferences

This paper investigates cluster-based cooperative spectrum sensing issues in two-layer hierarchical cognitive radio networks with soft data fusion. We first define a two-phase reporting protocol in the paper. In the first phase, secondary users forward their soft sensing information to cluster heads (CHs) over large-scale fading. In the second phase, all CHs transmit the aggregated soft energy information to the fusion center (FC) with different weights. Thus we derive the network false alarm (FA) and the detection probabilities as functions of the FC decision threshold, the clustering algorithm and different weights. Given a target on the detection probability, minimizing the FA probability is then formulated as a constraint optimization problem within two scenarios including additive white Gaussian noise environment and Rayleigh fading environment. A close-form upper bound of the FA probability is derived and a novel clustering scheme is also proposed for each scenario. Numerical results show that the proposed schemes achieve a satisfying performance.

Ying Wang

Papers

Joint Linear Filter Design in Multi-User Non-Regenerative MIMO-Relay Systems

Distributed Resource Allocation for D2D-Assisted Small Cell Networks With Heterogeneous Spectrum

Multi-leader Multi-follower Stackelberg Game Based Dynamic Resource Allocation for Mobile Cloud Computing Environment

Clustered device-to-device caching based on file preferences

Optimization of Cluster-Based Cooperative Spectrum Sensing Scheme in Cognitive Radio Networks with Soft Data Fusion