Ehud Lehrer

Bio: Ehud Lehrer is an academic researcher from Tel Aviv University. The author has contributed to research in topics: Repeated game & Stochastic game. The author has an hindex of 34, co-authored 96 publications receiving 3787 citations. Previous affiliations of Ehud Lehrer include INSEAD & Saint Petersburg State University.

Rational Learning Leads to Nash Equilibrium

Abstract: Two players are about to play a discounted infinitely repeated bimatrix game. Each player knows his own payoff matrix and chooses a strategy which is a best response to some private beliefs over strategies chosen by his opponent. If both players' beliefs contain a grain of truth (each assigns some positive probability to the strategy chosen by the opponent), then they will eventually (a) accurately predict the future play of the game and (b) play a Nash equilibrium of the repeated game. An immediate corollary is that in playing a Harsanyi-Nash equilibrium of a discounted repeated game of incomplete information about opponents' payoffs, the players will eventually play an equilibrium of the real game as if they had complete information.

Rational Learning Leads to Nash Equilibrium

Abstract: Each of n players, in an infinitely repeated game, starts with subjective beliefs about his opponents' strategies. If the individual beliefs are compatible with the true strategies chosen, then Bayesian updating will lead in the long run to accurate prediction of the future play of the game. It follows that individual players, who know their own payoff matrices and choose strategies to maximize their expected utility, must eventually play according to a Nash equilibrium of the repeated game. An immediate corollary is that, when playing a Harsanyi-Nash equilibrium of a repeated game of incomplete information about opponents' payoff matrices, players will eventually play a Nash equilibrium of the real game, as if they had complete information.

Subjective equilibrium in repeated games

Abstract: A player's strategy, for an n-person infinitely repeated game with discounting, is subjectively rational if it is a best response to his individual beliefs regarding opponents' strategies. A vector of such strategies is a subjective equilibrium if the play induced by it is realization equivalent to the play induced by each players' beliefs. Thus, any statistical updating can only reinforce the beliefs. It is shown that under perfect monitoring, the joint behavior at a subjective equilibrium approximates a behavior of a Nash equilibrium even when perturbations are allowed. Therefore, learning processes leading to subjective equilibrium result in approximate Nash behavior.(This abstract was borrowed from another version of this item.)

Prediction, learning, and games

Abstract: 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.

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

Abstract: 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

Foundations of Machine Learning

Abstract: This graduate-level textbook introduces fundamental concepts and methods in machine learning. It describes several important modern algorithms, provides the theoretical underpinnings of these algorithms, and illustrates key aspects for their application. The authors aim to present novel theoretical tools and concepts while giving concise proofs even for relatively advanced topics. Foundations of Machine Learning fills the need for a general textbook that also offers theoretical details and an emphasis on proofs. Certain topics that are often treated with insufficient attention are discussed in more detail here; for example, entire chapters are devoted to regression, multi-class classification, and ranking. The first three chapters lay the theoretical foundation for what follows, but each remaining chapter is mostly self-contained. The appendix offers a concise probability review, a short introduction to convex optimization, tools for concentration bounds, and several basic properties of matrices and norms used in the book. The book is intended for graduate students and researchers in machine learning, statistics, and related areas; it can be used either as a textbook or as a reference text for a research seminar.

Psychology and Economics

Abstract: UNTVERSITY OF CALIFORNIA AT BERKELEY Department of Economics Berkeley, CaHfornia 94720-3880 Working Paper No. 97-251 Psychology and Economics Matthew Rabin Department of Economics University of California, Berkeley January 1997 Key words: bounded rationality, decision making, fairness, framing effects, heuristics and biases, preferences, psychology, reciprocity, reference-dependent utility JEL Classification: A12, B49, D i l , D60, D81, D83, D91 This is a longer version of an essay under preparation for possible publication in the Journal of Economic Literature. I thank John Pencavel and anonymous referees for earlier comments on its structure and content. For comments on this draft, I thank Steven Blatt, Colin Camerer, Peter Diamond, Erik Eyster, Ernst Fehr, Danny Kahneman, George Loewenstein, Ted O'Donoghue, and John Pencavel. For helpful conversations over the past several years on topics covered in this essay, I thank George Akerlof, Gary Chamess, Eddie Dekel, Peter Diamond, David Laibson, David I. Levine, George Loewenstein, Rob MacCoun, James Montgomery, Vai-Lam Mui, Drazen Prelec, and especially Colin Camerer, Danny Kahneman, and Richard Thaler. Co-authors on research related to the topics of this essay include David Bowman, Deborah Minehart, Ted O'Donoghue, and Joel Schrag. Helpful research assistance was provided by Gadi Barlevy, Nikki Blasberg, Gail Brennan, Paul Ellickson, April Franco, Marcus Heng, Bruce Hsu, Jin Woo Jung, and especially Steven Blatt, Jimmy Chan, Erik Eyster, and Clara Wang. I am extremely grateful for financial support from the Russell Sage and Alfred P. Sloan Foundations.