/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

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

We introduce PIC, a practical coordinate-based mechanism to estimate Internet network distance (i.e., round-trip delay or network hops). Network distance estimation is important in many applications; for example, network-aware overlay construction and server selection. There are several proposals for distance estimation in the Internet but they all suffer from problems that limit their benefit. Most rely on a small set of infrastructure nodes that are a single point of failure and limit scalability. Others use sets of peers to compute coordinates but these coordinates can be arbitrarily wrong if one of these peers is malicious. While it may be reasonable to secure a small set of infrastructure nodes, it is unreasonable to secure all peers. PIC addresses these problems: it does not rely on infrastructure nodes and it can compute accurate coordinates even when some peers are malicious. We present PIC's design, experimental evaluation, and an application to network-aware overlay construction and maintenance.

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PIC: practical Internet coordinates for distance estimation

Existing indoor WiFi networks in the 2.5GHz and 5 GHz use too much transmit power, needed because the high carrier frequency limits signal penetration and connectivity. Instead, we propose a novel indoor wireless mesh design paradigm, based on Low Frequency, using the newly freed white spaces previously used as analogue TV bands, and Low Power - 100 times less power than currently used. Preliminary experiments show that this maintains a similar level of connectivity and performance to existing networks. It also yields more uniform connectivity, thus simplifies MAC and routing protocol design. We also advocate full-duplex networking in a single band, which becomes possible in this setting (because we operate at low frequencies). It potentially doubles the throughput of each link and eliminates hidden terminals.

https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/main-47.pdf

Rethinking Indoor Wireless Mesh Design: Low Power, Low Frequency, Full-Duplex

This paper describes a simple and robust ATM call admission control, and develops the theoretical background for its analysis. Acceptance decisions are based on whether the current load is less than a precalculated threshold, and Bayesian decision theory provides the framework for the choice of thresholds. This methodology allows an explicit treatment of the trade-off between cell loss and call rejection, and of the consequences of estimation error. Further topics discussed include the robustness of the control to departures from model assumptions, its performance relative to a control possessing precise knowledge of all unknown parameters, the relationship between leaky bucket depths and buffer requirements, and the treatment of multiple call types. >

A decision-theoretic approach to call admission control in ATM networks

This paper describes a framework for admission control for a packet-based network where the decisions are taken by edge devices or end-systems, rather than resources within the network. The decisions are based on the results of probe packets that the end-systems send through the network, and require only that resources apply a mark to packets in a way that is load dependent. One application example is the Internet, where marking information is fed back via an ECN bit, and we show how this approach allows a rich QoS framework for flows or streams. Our approach allows networks to be explicitly analyzed, and consequently engineered.

/pdf/distributed-admission-control-30qbf1ud9x.pdf

Distributed admission control

Recent advances in PHY layer design demonstrated efficient self-interference cancellation and full-duplex in a single band. Building a MAC that exploits self-interference cancellation is a challenging task. Links can be scheduled concurrently, but only if they either (i) don't interfere or (ii) allow for self-interference cancellation. Two issues arise: Firstly, it is difficult to construct a schedule that fully exploits the potentials for self-interference cancellation for arbitrary traffic patterns. Secondly, designing an efficient and fair distributed MAC is a daunting task; the issues become even more pronounced when scheduling under the constraints. We propose ContraFlow, a novel MAC that exploits the benefits of self-interference cancellation and increases spatial reuse. We use full-duplex to eliminate hidden terminals, and we rectify decentralized coordination inefficiencies among nodes, thereby improving fairness. Using measurements and simulations we illustrate the performance gains achieved when ContraFlow is used and we obtain both a throughput increase over current systems, as well as a significant improvement in fairness.

/pdf/efficient-and-fair-mac-for-wireless-networks-with-self-1u3arlwc05.pdf

Peter Key

Papers

PIC: practical Internet coordinates for distance estimation

Rethinking Indoor Wireless Mesh Design: Low Power, Low Frequency, Full-Duplex

A decision-theoretic approach to call admission control in ATM networks

Distributed admission control

Efficient and fair MAC for wireless networks with self-interference cancellation