There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

There is considerable pressure to define the key requirements of 5G, develop 5G standards, and perform technology trials as quickly as possible. Normally, these activities are best done in series but there is a desire to complete these tasks in parallel so that commercial deployments of 5G can begin by 2020. 5G will not be an incremental improvement over its predecessors; it aims to be a revolutionary leap forward in terms of data rates, latency, massive connectivity, network reliability, and energy efficiency. These capabilities are targeted at realizing high-speed connectivity, the Internet of Things, augmented virtual reality, the tactile internet, and so on. The requirements of 5G are expected to be met by new spectrum in the microwave bands (3.3-4.2 GHz), and utilizing large bandwidths available in mm-wave bands, increasing spatial degrees of freedom via large antenna arrays and 3-D MIMO, network densification, and new waveforms that provide scalability and flexibility to meet the varying demands of 5G services. Unlike the one size fits all 4G core networks, the 5G core network must be flexible and adaptable and is expected to simultaneously provide optimized support for the diverse 5G use case categories. In this paper, we provide an overview of 5G research, standardization trials, and deployment challenges. Due to the enormous scope of 5G systems, it is necessary to provide some direction in a tutorial article, and in this overview, the focus is largely user centric, rather than device centric. In addition to surveying the state of play in the area, we identify leading technologies, evaluating their strengths and weaknesses, and outline the key challenges ahead, with research test beds delivering promising performance but pre-commercial trials lagging behind the desired 5G targets.

5G : A tutorial overview of standards, trials, challenges, deployment, and practice

Simulation and the monte carlo method

: The problem of scattering by a triangular pyramid is studied using an extension of the geometrical theory of diffraction by the method of moments. Thus, the current distribution on the faces of the perfectly conducting pyramid is found by solving the three dimensional wedge diffraction problem once for each wedge, or a total of six times. This procedure yields the current in the GTD region on each face. The current near the edge of each wedge is then found using the moment method. The currents so obtained do not include that current caused by tip diffraction. The effect of this current on the far zone field may be added post facto using a formula given by Keller, et al. Results are shown for the bistatic radar cross section and in all cases the results are in good agreement with experimental measurements. (Author)

Bistatic scattering by a triangular pyramid

Summary form only given. The design problem of a linear antenna array has been in focus for many years. Several design techniques have been proposed which are described in standard textbooks. Among them is the orthogonal method that was initially proposed by Unz (1966) and subsequently applied by Sahalos (1974) to several design problems. The method is, general and guarantees an minimum mean square error approximation of the desired pattern. One of the problems related to linear array design is the quantization of amplitudes. Quantization is appropriate in arrays of solid-state modules with saturated output amplifiers. The main problem is to devise a method that is able to reduce the number of the independent amplitude levels while approximating the desired pattern in an optimal sense. We model the problem as a set partitioning combinatorial problem, in which each possible configuration is evaluated by the orthogonal method and a configuration is chosen that best approximates the desired pattern minimizing the mean square error. The total number of different configurations is given by a Striling number of the second kind. This means that even for a moderate number of elements the problem becomes computer intensive and it is appropriate to utilize possible symmetries that are known a priori to reduce the computation time. We present the formulation and several examples, demonstrating the applicability of the method.

On the independent amplitude, level reduction of a broadside linear array by the orthogonal method

Summary form only given. The computer aided analysis of passive microwave components using numerical techniques has received significant attention in the passed years. There is a number of available general purpose CAD tools but these in general can not be used for design purposes since they are very time consuming. In contrary, employing a dedicated mode matching scheme we could have an impressive increase in speed. This work aims exactly at the application of the mode matching technique developed in our previous work, to the analysis and synthesis of microwave components. For the validation of the present method a comparison with a general purpose commercial software package (HP-HFSS Finite Element) is carried out. A very good agreement is observed but our method is quite faster due to the availability of the involved integrals in closed form. Finally, numerical results are given for the case of a Ku band otrhomode transducer and a diplexer consisting of impedance transformers, power dividers and band pass filters. These devices are mainly designed using coaxial irises in a circular waveguide.

Analysis and design of waveguide components using a fast mode matching technique

The current work contributes a detailed design of overlapping element direct radiating arrays for satellite communications employing the elements on a planar host Direct radiating arrays are undisputedly considered as the next step in the space sector of communication industry but their advent is not without challenge Direct radiating arrays can provide the highly adaptive performance needed for extremely demanding terrestrial and satellite communication cases but unfortunately their cost is also high This cost is mainly due to the number of control points, (phase shifters plus amplifiers), needed to meet the specifications Thus the quest for this number reduction is ongoing Currently, there is a paradigm shift towards using not non-overlapping but overlapping radiating elements The current work addresses the problem and assesses the solution's potential

Design of overlapping element direct radiating arrays for satellite communications

Summary form only given. The circular and coaxial waveguide discontinuities were and still remain of great importance in the development of microwave networks. This is due to the fact that multiple discontinuities of these types can be used in the analysis of offset single or multiple coaxial irises in a circular waveguide. This basic geometry can be used in the design of high quality microwave networks like filters, impedance transformers and horn antennas. The offset coaxial iris requires the study of the discontinuity of a circular-to-an offset coaxial waveguide. This is exactly the purpose of the present work. It is important to note that this approach offers the possibility of the introduction of multiple offset coaxial irises on a single diaphragm. In turn this is expected to yield more compact microwave components. The analytical evaluation of the involved coupling integrals results in a very fast and accurate method that makes it appropriate to be included within microwave network synthesis algorithms. A number of geometries have been studied, including single and double offset coaxial irises. Some of them are presented for comparisons with commercial electromagnetic simulators in order to validate the proposed analytical formulation.

John N. Sahalos

Papers

Bistatic scattering by a triangular pyramid

On the independent amplitude, level reduction of a broadside linear array by the orthogonal method

Analysis and design of waveguide components using a fast mode matching technique

Design of overlapping element direct radiating arrays for satellite communications

Analytical characterization of the step discontinuity between a circular and an offset coaxial waveguide using the mode matching technique