Book:R. Duncan Luce/Games and Decisions
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R. Duncan Luce and Howard Raiffa: Games and Decisions: Introduction and Critical Survey
Published $\text {1957}$, Dover Publications, Inc.
- ISBN 0-486-65943-7
Subject Matter
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
Cited by
- 1991: Roger B. Myerson: Game Theory
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory
Source work progress
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