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

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

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

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

* The first tutorial-style book that gives all the relevant theory at the right level of rigor, for the wireless communications engineer. * Bridges the gap between theory and practice by giving examples and case studies showing how game theory can solve real-word problems. * Contains algorithms and techniques to implement game theory in wireless terminals. Written by leading experts in the field, Game Theory and Learning for Wireless Networks Covers how theory can be used to solve prevalent problems in wireless networks such as power control, resource allocation or medium access control. With the emphasis now on promoting 'green' solutions in the wireless field where power consumption is minimized, there is an added focus on developing network solutions that maximizes the use of the spectrum available. With the growth of distributed wireless networks such as Wi-Fi and the Internet; the push to develop ad hoc and cognitive networks has led to a considerable interest in applying game theory to wireless communication systems. Game Theory and Learning for Wireless Networks is the first comprehensive resource of its kind, and is ideal for wireless communications R&D engineers and graduate students. Samson Lasaulce is a senior CNRS researcher at the Laboratory of Signals and Systems (LSS) at Suplec, Gif-sur-Yvette, France. He is also a part-time professor in the Department of Physics at cole Polytechnique, Palaiseau, France. Hamidou Tembine is a professor in the Department of Telecommunications at Suplec, Gif-sur-Yvette, France. Merouane Debbah is a professor at Suplec, Gif-sur-Yvette, France. He is the holder of the Alcatel-Lucent chair in flexible radio since 2007. The first tutorial style book that gives all the relevant theory, at the right level of rigour, for the wireless communications engineer Bridges the gap between theory and practice by giving examples and case studies showing how game theory can solve real world resource allocation problems Contains algorithms and techniques to implement game theory in wireless terminals

Game Theory and Learning for Wireless Networks: Fundamentals and Applications

We consider a noncooperative interaction among a large population of mobiles that interfere with each other through many local interactions. The first objective of this paper is to extend the evolutionary game framework to allow an arbitrary number of mobiles that are involved in a local interaction. We allow for interactions between mobiles that are not necessarily reciprocal. We study 1) multiple-access control in a slotted Aloha-based wireless network and 2) power control in wideband code-division multiple-access wireless networks. We define and characterize the equilibrium (called evolutionarily stable strategy) for these games and study the influence of wireless channels and pricing on the evolution of dynamics and the equilibrium.

Evolutionary Games in Wireless Networks

Underwater communication remains a challenging technology via communication cables and the cost of underwater sensor network (UWSN) deployment is still very high. As an alternative, underwater wireless communication has been proposed and have received more attention in the last decade. Preliminary research indicated that the Radio Frequency (RF) and Magneto-Inductive (MI) communication achieve higher data rate in the near field communication. The optical communication achieves good performance when limited to the line-of-sight positioning. The acoustic communication allows long transmission range. However, it suffers from transmission losses and time-varying signal distortion due to its dependency on environmental properties. These latter are salinity, temperature, pressure, depth of transceivers, and the environment geometry. This paper is focused on both the acoustic and magneto-inductive communications, which are the most used technologies for underwater networking. Such as acoustic communication is employed for applications requiring long communication range while the MI is used for real-time communication. Moreover, this paper highlights the trade-off between underwater properties, wireless communication technologies, and communication quality. This can help the researcher community by providing clear insight for further research.

Underwater Wireless Sensor Networks: A Survey on Enabling Technologies, Localization Protocols, and Internet of Underwater Things

In this article, we investigate the competitive interaction between electrical vehicles or hybrid oil-electricity vehicles in a Cournot market consisting of electricity transactions to or from an underlying electricity distribution network. We provide a mean field game formulation for this competition, and introduce the set of fundamental differential equations ruling the behavior of the vehicles at the feedback Nash equilibrium, referred here to as the mean field equilibrium. This framework allows for a consistent analysis of the evolution of the price of electricity as well as of the instantaneous electricity demand in the power grid. Simulations precisely quantify those parameters and suggest that significant reduction of the daily electricity peak demand can be achieved by appropriate electricity pricing.

https://hal-supelec.archives-ouvertes.fr/hal-00769395/document

Electrical Vehicles in the Smart Grid: A Mean Field Game Analysis

Establishing the link between several theories, this book demonstrates what is needed to learn strategic interaction in wireless networks under uncertainty, randomness, and time delays. This robust game theory cookbook analyzes games where some parameters are uncertain and random. Starting with the fundamentals of strategic learning and game theory, the text then covers partially and fully distributed learning, combined learning for negotiation, bargaining solutions, Nash equilibria, Stackelberg solutions, correlated equilibria, conjectural variations, and satisfactory solutions. It concludes with practical algorithms and techniques to implement game theory in wireless networks.

/pdf/distributed-strategic-learning-for-wireless-engineers-mh0irz66it.pdf

Hamidou Tembine

Papers

Game Theory and Learning for Wireless Networks: Fundamentals and Applications

Evolutionary Games in Wireless Networks

Underwater Wireless Sensor Networks: A Survey on Enabling Technologies, Localization Protocols, and Internet of Underwater Things

Electrical Vehicles in the Smart Grid: A Mean Field Game Analysis

Distributed Strategic Learning for Wireless Engineers