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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 letter considers a downlink spectrum sharing cognitive radio (CR) multicast network coexisting with a primary network. The problem of joint power and rate allocation to maximize the average sum rate is studied. In this regard, a joint power and rate allocation scheme is proposed, where the allocated rate can be higher than the lowest rate of all the secondary users (SUs) within the same group, which is different from the conventional multicast transmission scheme. To guarantee the quality of service (QoS) of the SU, the service outage probability defined as the probability that the maximum achievable rate of the SU is lower than the rate of the group, is constrained to be under a certain threshold, which is termed as the service outage constraint. The numerical results show that the proposed scheme provides significant improvement over the conventional scheme in terms of average sum rate.

Joint power and rate allocation for spectrum sharing cognitive radio multicast networks under service outage constraint

Ultra-reliable and low-latency communication (URLLC) is proposed as one of the three key services of 5G for Internet of Things (IoT), especially for mission-critical applications This paper investigates the minimum power of devices in uplink in IoT networks for URLLC Unmanned aerial vehicles (UAVs) are utilized to assistant the IoT system because they have flexible deployment and high probability to establish line-of-sight (LoS) communication links First, we formulate a minimum average transmit power problem under the constraints of latency and reliability in modern industry The deployment of UAVs and device association need to be jointly optimized, making the problem non-linear and non-convex Then the block error probability which characterizes the reliability is derived under finite blocklength regime and an iteration algorithm is proposed Additionally, the minimum average transmit power of IoT devices in URLLC is also calculated by deploying different number of UAVs Simulation results are presented to show that the transmit power can be greatly reduced by appropriately deploying more UAVs or relaxing the tolerance of latency

Power Limited Ultra-Reliable and Low-Latency Communication in UAV-Enabled IoT Networks

We consider relay selection technique in a cooperative cellular network where user terminals act as mobile relays to help the communications between base station (BS) and mobile station (MS). A novel relay selection scheme, called Joint Uplink and Downlink Relay Selection (JUDRS), is proposed in this paper. Specifically, we generalize JUDRS in two key aspects: (i) relay is selected jointly for uplink and downlink, so that the relay selection overhead can be reduced, and (ii) we consider to minimize the weighted total energy consumption of MS, relay and BS by taking into account channel quality and traffic load condition of uplink and downlink. Information theoretic analysis of the diversity-multiplexing tradeoff demonstrates that the proposed scheme achieves full spatial diversity in the quantity of cooperating terminals in this network. And numerical results are provided to further confirm a significant energy efficiency gain of the proposed algorithm comparing to the previous best worse channel selection and best harmonic mean selection algorithms.

Joint Uplink and Downlink Relay Selection in Cooperative Cellular Networks

Pre-caching popular files at mobile users with the aid of device-to-device (D2D) communications can offload the data traffic to low-cost D2D links and reduce the network transmission cost. This leads to additional cache leasing cost brought by the lease of storage from mobile users. Besides, newly-emerging video-related applications also pose strict requirement on the network delay. Thus, it is of great significance to design caching strategies considering the transmission cost, the cache leasing cost and the delay. As the movement of mobile users can improve the communication opportunities among different users and increase the cache hit ratio, in this paper, mobility-aware caching strategies are designed to minimize the network cost including both the transmission cost and the cache leasing cost with the delay constraint. In specific, by characterizing the user mobility as an inter-contact model, analytical expressions of the average network cost and the average file delivery delay are derived and a cost-oriented mobility-aware caching problem is formulated. To handle this mixed integer nonlinear programming (MINLP) problem, we first relax the binary cache placement indicator as a continuous one and prove that both the average network cost and the average file delivery delay are convex. Hence, an iterative caching algorithm is proposed with the successive convex approximation method. Moreover, to lower the complexity, combinatorial optimization method is adopted. Firstly, to make the caching problem tractable, the average file delivery delay constraint is implicitly added in the cost objective function as a penalty term. Then, the reformulated objective function is proved to have the non-monotone submodular property and thus a modified low-complexity greedy caching strategy is proposed. Simulation results show that, compared with the most popular caching strategy, our proposed mobility-aware caching strategy can reduce the average cost by 46% when the user speed is high.

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Cost-Oriented Mobility-Aware Caching Strategies in D2D Networks With Delay Constraint

This paper focuses on adaptive resource scheduling for multiple services per user at the downlink of multiple input multiple output (MIMO) - orthogonal frequency division multiplexing (OFDM) system. In future wireless networks, one user will simultaneously require multiple homogeneous or heterogeneous services. Then, the scheduling algorithm is responsible for not only assigning resource blocks to different users but also distributing the assigned resource blocks among multiple services for one user. This paper firstly formulates this integrated optimization problem based on utility function in homogeneous service system. As the solution to the optimization problem requires high computational complexity, a sub-optimal and low-complexity algorithm is proposed with two theorems for practical implementation. Moreover, the algorithm is extended to heterogeneous services system by classifying delay sensitive services according to the head-of-line packets delay. The design goal of the algorithm is to fully exploit multiuser diversity gain while guaranteeing the quality of service (QoS) for delay sensitive services. Numeric results show that the algorithm outperforms traditional algorithm in terms of system spectral efficiency and fairness criterion.

Ying Wang

Papers

Joint power and rate allocation for spectrum sharing cognitive radio multicast networks under service outage constraint

Power Limited Ultra-Reliable and Low-Latency Communication in UAV-Enabled IoT Networks

Joint Uplink and Downlink Relay Selection in Cooperative Cellular Networks

Cost-Oriented Mobility-Aware Caching Strategies in D2D Networks With Delay Constraint

Utility Based Scheduling Algorithm for Multiple Services Per User in MIMO OFDM System