Book:R. Duncan Luce/Games and Decisions

Subject Matter

 * Game Theory

Contents

 * Preface


 * 1 General Introduction to the Theory of Games
 * 1.1 CONFLICT OF INTERESTS
 * 1.2 HISTORICAL BACKGROUNDS
 * 1.3 AN INFORMAL CHARACTERIZATION OF A GAME
 * 1.4 EXAMPLES OF CONFLICT OF INTEREST
 * 1.5 GAME THEORY AND THE SOCIAL SCIENTIST


 * 2 Utility Theory
 * 2.1 A CLASSIFICATION OF DECISION MAKING
 * 2.2 INDIVIDUAL DECISION MAKING UNDER CERTAINTY
 * *2.3 AN EXAMPLE OF DECISION MAKING UNDER CERTAINTY: LINEAR PROGRAMMING
 * 2.4 INDIVIDUAL DECISION MAKING UNDER RISK
 * 2.5 AN AXIOMATIC TREATMENT OF UTILITY
 * 2.6 SOME COMMON FALLACIES
 * 2.7 INTERPERSONAL COMPARISONS OF UTILITY
 * *2.8 EXPERIMENTAL DETERMINATIONS OF UTILITY
 * 2.9 SUMMARY


 * 3 Extensive and Normal Forms
 * 3.1 GAME TREES
 * 3.2 INFORMATION SETS
 * 3.3 OUTCOMES
 * 3.4 AN EXAMPLE: THE GAME OF GOPS
 * 3.5 EXTENSIVE FORM
 * 3.6 RATIONALITY AND KNOWLEDGE
 * 3.7 PURE STRATEGIES AND THE NORMAL FORM
 * 3.8 SUMMARY


 * 4 Two-person Zero-sum Games
 * 4.1 INTRODUCTION
 * 4.2 STRICTLY COMPETITIVE AND NON-STRICTLY COMPETITIVE GAMES
 * 4.3 REASONING ABOUT STRICTLY COMPETITIVE GAMES
 * 4.4 AN A PRIORI DEMAND OF THE THEORY
 * 4.5 GAMES WITH EQUILIBRIUM PAIRS
 * *4.6 EQUILIBRIUM PAIRS IN EXTENSIVE GAMES
 * 4.7 GAMES WITHOUT EQUILIBRIUM PAIRS
 * 4.8 THE MINIMAX THEOREM
 * 4.9 COMPATIBILITY OF THE PURE AND MIXED STRATEGY THEORIES
 * 4.10 ON THE INTERPRETATION OF A MIXED STRATEGY
 * 4.11 EXPLOITATION OF OPPONENT'S WEAKNESSES
 * *4.12 A GUIDE TO THE APPENDICES ON TWO-PERSON ZERO-SUM GAMES
 * 4.13 SUMMARY


 * 5 Two-person Non-zero-sum Non-cooperative Games
 * 5.1 INTRODUCTION
 * 5.2 REVIEW OF THE SALIENT ASPECTS OF ZERO-SUM GAMES
 * 5.3 AN EXAMPLE: BATTLE OF THE SEXES
 * 5.4 AN EXAMPLE: THE PRISONER'S DILEMMA
 * 5.5 TEMPORAL REPETITION OF THE PRISONER'S DILEMMA
 * 5.6 ITERATIONS OF ZERO-SUM GAMES
 * 5.7 THE ROLE OF EQUILIBRIUM PAIRS IN NON-ZERO-SUM GAMES
 * *5.8 EXISTENCE OF EQUILIBRIUM PAIRS
 * *5.9 DEFINITIONS OF "SOLUTION" FOR NON-COOPERATIVE GAMES
 * 5.10 SOME PSYCHOLOGICAL FEATURES
 * 5.11 DESIRABILITY OF PREPLAY COMMUNICATION
 * 5.12 SUMMARY


 * Two-person Cooperative Games
 * 6.1 INTRODUCTION
 * 6.2 THE VON NEUMANN-MORGENSTERN SOLUTION
 * 6.3 SOLUTIONS-IN WHAT SENSE?
 * 6.4 ARBITRATION SCHEMES
 * 6.5 NASH'S BARGAINING PROBLEM
 * 6.6 CRITICISMS OF NASH'S MODEL OF THE BARGAINING PROBLEM
 * 6.7 ALTERNATIVE APPROACHES TO THE BARGAINING PROBLEM
 * 6.8 ARBITRATION SCHEMES FOR NON-STRICTLY COMPETITIVE GAMES: THE SHAPLEY VALUE
 * 6.9 ARBITRATION SCHEMES FOR NON-STRICTLY COMPETITIVE GAMES: NASH'S EXTENDED BARGAINING MODEL
 * 6.10 ARBITRATION SCHEMES FOR NON-STRICTLY COMPETITIVE GAMES: THE CASE OF MEANINGFUL INTERPERSONAL COMPARISONS OF UTILITY
 * 6.11 TWO DEFINITIONS OF INTERPERSONAL COMPARISONS IN TWO-PERSON GAMES
 * *6.12 STABILITY OF ARBITRATION SCHEMES
 * 6.13 SUMMARY


 * 7 Theories of $$n$$-Person Games in Normal Form
 * 7.1 INTRODUCTION
 * 7.2 MIXED STRATEGIES AND THE NORMAL FORM
 * 7.5 CONSTANT-SUM AND ZERO-SUM GAMES
 * *7.4 BEHAVIORAL STRATEGIES AND PERFECT RECALL
 * *7.5 COMPOSITE STRATEGIES
 * 7.6 COMMUNICATION BOUNDARY CONDITIONS
 * 7.7 CLASSIFICATION OF CONTEXTS FOR $$n$$-PERSON GAMES
 * *7.8 NON-COOPERATIVE GAMES: EOUILIBRIUM POINTS
 * 7.9 COOPERATIVE GAMES WITHOUT SIDE PAYMENTS
 * 7.10 SUMMARY


 * 8 Characteristic Functions
 * 8.1 SIDE PAYMENTS
 * 8.2 DEFINITION OF CHARACTERISTIC FUNCTION
 * 8.3 $$S$$-EQUIVALENCE AND NORMALIZATION OF CHARACTERISTIC FUNCTIONS
 * *8.4 SET FUNCTIONS
 * 8.5 CRITICISM
 * 8.6 IMPUTATIONS AND THE CORE
 * 8.7 SUMMARY


 * 9 Solutions
 * 9.1 THE VON NEUMANN-MORGENSTERN DEFINITION OF A SOLUTION
 * 9.2 SOME REMARKS ABOUT THE DEFINITION
 * 9.3 SOME IMPLICATIONS OF THE DEFINITION
 * 9.4 THE SOLUTIONS OF A MARKET WITH ONE SELLER AND TWO BUYERS
 * 9.5 FURTHER RESULTS ON SOLUTIONS
 * 9.6 STRONG SOLUTIONS
 * *9.7 SOLUTIONS OVER DOMAINS DIFFERENT FROM IMPUTATIONS
 * 9.8 SUMMARY


 * 10 $$\psi$$-Stability
 * 10.1 $$\psi$$-STABLE PAIRS
 * 10.2 CRITICISM
 * 10.3 THE $$\psi$$-STABILITY OF ANALYSIS OF A MARKET WITH ONE SELLER AND TWO BUYERS
 * 10.4 NON-TRANSFERABLE UTILITIES
 * 10.5 SUMMARY


 * 11 Reasonable Outcomes and Value
 * 11.1 REASONABLE OUTCOMES: THE CLASS $$B$$
 * 11.2 REASONABLE OUTCOMES: THE CLASS $$L$$
 * 11.3 REASONABLE OUTCOMES: THE CLASS $$D$$
 * 11.4 VALUE
 * 11.5 VALUE AS AN ARBITRATION SCHEME


 * 12 Applications of $$n$$-Person Theory
 * 12.1 THE A PRIORI POWER DISTRIBUTIONS OF VOTING SCHEMES
 * 12.2 POWER DISTRIBUTIONS IN AN IDEALIZED LEGISLATURE
 * 12.3 AN EXPERIMENT
 * 12.4 ARE "REAL" GAMES EVER "ABSTRACT" GAMES?


 * 13 Individual Decision Making under Uncertainty
 * 13.1 INTRODUCTION AND STATEMENT OF PROBLEM
 * 13.2 SOME DECISION CRITERIA
 * 13.3 AXIOMATIC TREATMENT: THE AXIOMS NOT REFERRING TO "COMPLETE IGNORANCE"
 * 13.4 AXIOMATIC TREATMENT: THE AXIOMS REFERRING TO "COMPLETE IGNORANCE"
 * 13.5 THE CASE OF "PARTIAL IGNORANCE"
 * 13.6 GAMES AS DECISION MAKING UNDER UNCERTAINTY
 * 13.7 STATISTICAL DECISION MAKING - FIXED EXPERIMENTATION
 * 13.8 STATISTICAL DECISION MAKING - EXPERIMENTATION NOT FIXED
 * 13.9 COMPLETE CLASSES OF DECISION RULES
 * 13.10 CLASSICAL STATISTICAL INFERENCE VERSUS MODERN STATISTICAL DECISION THEORY: SOME VERY BRIEF COMMENTS
 * 13.11 SUMMARY


 * 14 Group Decision Making
 * 14.1 INTRODUCTION
 * 14.2 SOCIAL CHOICE AND INDIVIDUAL VALUES: PRELIMINARY STATEMENT
 * 14.3 GENERAL FORMULATION OF PROBLEM
 * 14.4 CONDITIONS ON THE SOCIAL WELFARE FUNCTION AND ARROW'S IMPOSSIBILITY THEOREM
 * 14.5 DISCUSSION OF THE ARROW PARADOX
 * 14.6 SOCIAL CHOICE PROCEDURES BASED ON INDIVIDUAL STRENGTHS OF PREFERENCES
 * 14.7 MAJORITY RULE AND RESTRICTED PROFILES
 * 14.8 STRATEGIC ASPECTS OF MAJORITY RULE
 * 14.9 GAMES OF FAIR DIVISION
 * 14.10 SUMMARY


 * APPENDICES


 * I A Probabilistic Theory of Utility
 * A1.1 INTRODUCTION
 * A1.2 PREFERENCE DISCRIMINATION AND INDUCED PREFERENCE
 * A1.3 LIKELIHOOD DISCRIMINATION AND QUALITATIVE PROBABILITY
 * A1.4 THE UTILITY AND SUBJECTIVE PROBABILITY FUNCTIONS
 * A1.5 CONCLUSIONS ABOUT THE SUBJECTIVE SCALES
 * A1.6 AN IMPOSSIBILITY THEOREM


 * 2 The Minimax Theorem
 * A2.1 STATEMENT OF THE PROBLBM
 * A2.2 HISTORICAL REMARKS
 * A2.3 NASH's PROOF or THE MINIMAX THEOREM


 * 3 First Geometrical Interpretation of a Two-person Zero-Sum Game


 * 4 Second Geometrical Interpretation of a Two-person Zero-Sum Game


 * 5 Linear Programing and Two-Person Zero-Sum Games
 * A5.1 REDUCTION OF A GAME TO A LINEAR-PROGRAMING PROBLEM
 * A5.2 DUALITY THEORY OF THE GENERAL LINEAR-PROGRAMING PROBLEM
 * A5.3 REDUCTION OF A LINEAR-PROGRAMING PROBLEM TO A GAME


 * 6 Solving Two-person Zero-sum Games
 * A6.1 INTRODUCTION
 * A6.2 TRIAL AND ERROR
 * A6.3 CHECKING ALL CRITICAL POINTS
 * A6.4 THE DOUBLE DESCRIPTION METHOD
 * A6.5 THE SIMPLEX METHOD
 * A6.6 A GEOMETRIC INTERPRETATION OF THE SIMPLEX AND DUAL SIMPLEX PROCEDURES
 * A6.7 DIFFERENTIAL EQUATION SOLUTIONS OF SYMMETRIC GAMES
 * A6.8 SYMMETRIZATION OF A GAME
 * A6.9 ITERATIVE SOLUTION OF GAMES BY FICTITIOUS PLAY


 * 7 Games with Infinite Pure Strategy Sets
 * A7.1 INTRODUCTION
 * A7.2 GAMES WITH NO VALUE
 * A7.3 GAMES WHERE $$A$$ (OR $$B$$) IS FINITE
 * A7.4 GAMES WHERE $$A$$ IS "ALMOST" FINITE
 * A7.5 GAMES OVER THE UNIT SQUARE
 * A7.6 GAMES INVOLVING TIMING OR PARTITIONING
 * A7.7 A MODEL OF POKER DUE TO BOREL


 * 8 Sequential Compounding of Two-person Games
 * A8.1 INTRODUCTION
 * A8.2 STOCHASTIC GAMES
 * A8.3 RECURSIVE GAMES
 * A8.4 GAMES OF SURVIVAL
 * A8.5 MULTICOMPONENT ATTRITION GAMES
 * A8.6 APPROACHABILITY-EXCLUDABILITY THEORY AND COMPOUND DECISION PROBLEMS
 * A8.7 DIVIDEND POLICY AND ECONOMIC RUIN GAMES


 * Bibliography


 * Index