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Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

Cover

Title Page

Copyright Page

Dedication

Preface

Contents

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 Programing

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

6 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

7.3 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: Equilibrium 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 ψ-Stability

10.1 ψ-Stable Pairs

10.2 Criticism

10.3 The ψ-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

1 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 Problem

A2.2 Historical Remarks

A2.3 Nash's Proof of 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 Appro Ach Ability-Exclud Ability Theory and Compound Decision Problems

A8.7 Dividend Policy and Economic Ruin Games

Bibliography

Index

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书籍介绍

Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.