COLLECTED PAPERS Volume I
Robert J. Aumann
The MIT Press Cambridge, Massachusetts London, England Contents of Volume I
Preface ix
I GENERAL 1
1 What Is Game Theory Trying to Accomplish? 5 2 Game Theory 47 3 The Game of Politics: A Review of Rapoport's Fights, Games, and Debates 107 4 CORE as a Macrocosm of Game-Theoretic Research, 1967-1987 119 5 Arrow—the Breadth, Depth, and Conscience of the Scholar: An Interview 131 6 Economic Theory and Mathematical Method: An Interview 135 7 Report of the Committee on Election Procedures for Fellows 145 with M. Bruno, F. Hahn, and A. Sen 8 Foreword to A General Theory of Equilibrium Selection in Games 153 9 Foreword to Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis 157
II KNOT THEORY 159
10 Asphericity of Alternating Knots 163
III DECISION THEORY: UTILITY AND SUBJECTIVE PROBABILITY 183
11 The Coefficients in an Allocation Problem 193 with J. B. Kruskal 12 Assigning Quantitative Values to Qualitative Factors in the Naval Electronics Problem 209 with J. B. Kruskal 13 Subjective Programming 231 14a Utility Theory without the Completeness Axiom 257 14b Utility Theory without the Completeness Axiom: A Correction 275 15 Measurable Utility and the Measurable Choice Theorem 279 16 Linearity of Unrestrictedly Transferable Utilities 291 17 A Definition of Subjective Probability 295 with F. J. Anscombe vi Contents
18 Letter from Robert Aumann to Leonard Savage and Letter from Leonard Savage to Robert Aumann 305 19 The St. Petersburg Paradox: A Discussion of Some Recent Comments 311
IV STRATEGIC GAMES: REPEATED 315
20 Acceptable Points in General Cooperative /i-Person Games 321 21 Acceptable Points in Games of Perfect Information 355 22 Long-Term Competition—A Game-Theoretic Analysis 395 with L. S. Shapley 23 Survey of Repeated Games 411 24 Cooperation and Bounded Recall 439 with S. Sorin
25 Rationality and Bounded Rationality 475
V STRATEGIC GAMES: EXTENSIVE 489
26 A Characterization of Game Structures of Perfect Information 493 27 Almost Strictly Competitive Games 495 28 Mixed and Behavior Strategies in Infinite Extensive Games 503 29 Some Thoughts on the Minimax Principle 523 with M. Maschler 30 Approximate Purification of Mixed Strategies 533 with Y. Katznelson, R. Radner, R. Rosenthal, and B. Weiss
VI STRATEGIC EQUILIBRIUM AND THE THEORY OF KNOWLEDGE 553
31 Subjectivity and Correlation in Randomized Strategies 559 32 Agreeing to Disagree 593 33 Correlated Equilibrium as an Expression of Bayesian Rationality 597 34 Nash Equilibria Are Not Self-Enforcing 615 35 Irrationality in Game Theory 621 36 Backward Induction and Common Knowledge of Rationality 635 37 Epistemic Conditions for Nash Equilibrium 649 with A. Brandenburger vii Contents
Author Index 669 Journal Index 671 Citation Index 673 Name Index 753 Subject Index 761
Contents of Volume II
Preface VII Coalitional Games: The NTU Form 38 Von Neumann-Morgenstern Solutions to Cooperative Games without Side Payments with B. Peleg 39 The Core of a Cooperative Game without Side Payments 40 Introduction to "Some Thoughts on the Theory of Cooperative Games" 41 A Survey of Cooperative Games without Side Payments VIII Coalitional Games: Bargaining Set, Kernel, Nucleolus 42 The Bargaining Set for Cooperative Games with M. Maschler 43 A Method of Computing the Kernel of ^-Person Games with B. Peleg and P. Rabinowitz 44 Cooperative Games with Coalition Structures with J. Dreze 45 Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud with M. Maschler IX Coalitional Games: Core and Equilibria of Markets 46 Markets with a Continuum of Traders 47 Existence of Competitive Equilibria in Markets with a Continuum of Traders 48 Disadvantageous Monopolies 49 A Note on Gale's Example with B. Peleg 50 On the Rate of Convergence of the Core X Coalitional Games: Economic and Political Applications of the Shapley Value 51 Values of Markets with a Continuum of Traders 52 Power and Taxes with M. Kurz 53 Power and Taxes in a Multi-Commodity Economy with M. Kurz 54 Core and Value for a Public Goods Economy: An Example with R. J. Gardner and R. W. Rosenthal 55 Power and Public Goods with M. Kurz and A. Neyman 56 Voting for Public Goods with M. Kurz and A. Neyman 57 Values of Markets with Satiation or Fixed Prices with J. Dreze 58 Economic Applications of the Shapley Value 59 Endogenous Formation of Links between Players and of Coalitions: An Application of the Shapley Value with R. Myerson Contents
XI Coalitional Games: Foundations of the NTU Shapley Value 60 An Axiomatization of the Non-Transferable Utility Value 61a Values for Games without Side Payments: Some Difficulties with Current Concepts, by Alvin Roth 61b On the Existence and Interpretation of Value Allocation, by Wayne Shafer 61c On the Non-Transferable Utility Value: A Comment on the Roth-Shafer Examples 61 d On the Non-Transferable Utility Value: A Reply to Aumann, by Alvin Roth 61e Rejoinder 62a Non-Symmetric Cardinal Value Allocations, by Allen Scafuri and Nicholas Yannelis 62b Value, Symmetry, and Equal Treatment: A Comment on Scafuri and Yannelis XII Coalitional Games: Surveys of Value Theory 63 Recent Developments in the Theory of the Shapley Value 64 The Shapley Value XIII Mathematical Methods 65 Spaces of Measurable Transformations 66 Borel Structures for Function Spaces 67 On Choosing a Function at Random 68 Integrals of Set-Valued Functions 69 An Elementary Proof that Integration Preserves Uppersemicontinuity 70 A Variational Problem Arising in Economics with M. Perles 71 Random Measure Preserving Transformations 72 Orderable Set Functions and Continuity III: Orderability and Absolute Con- tinuity with U. Rothblum 73 Bi-Convexity and Bi-Martingales with S. Hart A duplicate Author Index, Journal Index, Citation Index, Name Index, and Subject Index appear in each volume.