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 $1957$, 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


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