A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.

A Course in Game Theory

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Convex Analysisの二,三の進展について

This important text and reference for researchers and students in machine learning, game theory, statistics and information theory offers a comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class. The central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems are viewed as instances of the experts' framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections.

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Prediction, learning, and games

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

Economics has much to do with incentives--not least, incentives to work hard, to produce quality products, to study, to invest, and to save. Although Adam Smith amply confirmed this more than two hundred years ago in his analysis of sharecropping contracts, only in recent decades has a theory begun to emerge to place the topic at the heart of economic thinking. In this book, Jean-Jacques Laffont and David Martimort present the most thorough yet accessible introduction to incentives theory to date. Central to this theory is a simple question as pivotal to modern-day management as it is to economics research: What makes people act in a particular way in an economic or business situation? In seeking an answer, the authors provide the methodological tools to design institutions that can ensure good incentives for economic agents. This book focuses on the principal-agent model, the "simple" situation where a principal, or company, delegates a task to a single agent through a contract--the essence of management and contract theory. How does the owner or manager of a firm align the objectives of its various members to maximize profits? Following a brief historical overview showing how the problem of incentives has come to the fore in the past two centuries, the authors devote the bulk of their work to exploring principal-agent models and various extensions thereof in light of three types of information problems: adverse selection, moral hazard, and non-verifiability. Offering an unprecedented look at a subject vital to industrial organization, labor economics, and behavioral economics, this book is set to become the definitive resource for students, researchers, and others who might find themselves pondering what contracts, and the incentives they embody, are really all about.

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The Theory of Incentives: The Principal-Agent Model

The Nash equilibrium concept may be extended gradually when the rules of the game are interpreted in a wider and wider sense, so as to allow preplay or even intraplay communication. A well-known extension of the Nash equilibrium is Aumann's correlated equilibrium, which depends only on the normal form of the game. Two other solution concepts for multistage games are proposed here: the extensive form correlated equilibrium, where the players can observe private extraneous signals at every stage and the communication equilibrium, where the players are furthermore allowed to transmit inputs to an appropriate device at every stage. We show that the set of payoffs associated with each solution concept has a canonical representation (in the spirit of the revelation principle) and is a convex polyhedron. We also provide for each concept a "super-canonical" game such that the set of payoffs associated with the solution concept is precisely the set of Nash equilibrium payoffs of this game.

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An approach to communication equilibria

Afriat (1967) showed the equivalence of the strong axiom of revealed preference and the existence of a solution to a set of linear inequalities. From this solution he constructed a utility function rationalizing the choices of a competitive consumer. We extend Afriat's theorem to a class of nonlinear budget sets. We obtain testable implications of rational behavior for a wide class of economic environments, and a constructive method to derive individual preferences from observed choices. In an application to market games, we identify a set of observable restrictions characterizing Nash equilibrium outcomes.

Afriat's Theorem for General Budget Sets

Aumann's (1987) theorem shows that correlated equilibrium is an expression of Bayesian rationality. We extend this result to games with incomplete information.

Five legitimate definitions of correlated equilibrium in games with incomplete information

Afriat's theorem for general budget sets

We study (costless) information transmission from a job applicant to an employer who must decide whether to hire him and, if so, which position to give him. We construct equilibrium payoffs requiring at least two signaling steps, or even that no deadline be imposed on the (plain) conversation. The set of communication equilibrium payoffs (achieved with the help of a communication device) is larger than the set of equilibrium payoffs of the plain conversation game but coincides with the set of correlated equilibrium payoffs.

Françoise Forges

Papers

An approach to communication equilibria

Afriat's Theorem for General Budget Sets

Five legitimate definitions of correlated equilibrium in games with incomplete information

Afriat's theorem for general budget sets

Equilibria with Communication in a Job Market Example