Game Theory and its Applications in the Social and Biological Sciences
Second Edition
Andrew M. Colman
1995, Oxford: Butterworth-Heinemann. Pp. xiv + 375. ISBN 0-7506-2369-1
Contents
Preface to the first edition
Preface to the second edition
BACKGROUND
1.
Introduction
1.1 Intuitive Background
1.1.1 Head On
1.1.2 Price War
1.1.3 Angelo and Isabella
1.2 Abstract Models: Basic
Terminology
1.3 Skill, Chance, Strategy
1.4 Historical Background
1.5 Summary
2.
One-Person Games
2.1 Games Against Nature
2.2 Certainty
2.3 Risk
2.4 Expected Utility Theory
2.5 Uncertainty
2.5.1 Insufficient Reason
2.5.2 Maximax
2.5.3 Maximin
2.5.4 Minimax Regret
2.6 Summary
3.
Coordination Games and the Minimal Social Situation
3.1 Strategic Collaboration
3.2 Coordination Games
3.3 The Minimal Social Situation
3.4 The Multi-Person Minimal Social Situation
3.5 Summary
THEORY AND EMPIRICAL EVIDENCE
4.
Two-Person Zero-Sum Games
4.1 Strictly Competitive Games
4.2 Extensive and Normal Forms
4.3 Games With Saddle Points: Nash Equilibria
4.4 Games Without Saddle Points
4.5 Dominance and Admissibility
4.6 Methods for Finding Solutions
4.7 Ordinal Payoffs and Incomplete Information
4.8 Summary
5.
Experiments With Strictly Competitive Games
5.1 Ideas Behind Experimental Games
5.2 Empirical Research on Non-Saddle-Point Games
5.3 Empirical Research on Saddle-Point Games
5.4 Framing Effects
5.5 Critique of Experimental Gaming
5.6 Summary
6.
Two-Person Mixed-Motive Games: Informal Game Theory
6.1 Mixed-Motive Games
6.2 Subgame Perfect and Trembling-Hand Equilibria
6.3 Classification of 2 ´ 2 Mixed-Motive Games
6.4 Leader
6.5 Battle of the Sexes
6.6 Chicken
6.7 Prisoner's Dilemma
6.8 Comparison of Archetypal 2 ´ 2 Games
6.9 Theory of Metagames
6.10 Two-Person Cooperative Games: Bargaining
Solutions
6.10.1 Maximin Bargaining
Solution
6.10.2 Nash Bargaining
Solution
6.10.3
Raiffa-Kalai-Smorodinsky Bargaining Solution
6.11 Summary
7.
Experiments With Prisoner's Dilemma and Related Games
7.1 The Experimental Gaming Literature
7.2 Strategic Structure
7.3 Payoffs and Incentives
7.4 Communication Effects
7.5 Programmed Strategies
7.6 Axelrod's Computer Tournaments
7.7 Sex Differences and Cross-Cultural Studies
7.8 Attribution Effects
7.9 Framing Effects
7.10 Summary
8.
Multi-Person Cooperative Games: Coalition Formation
8.1 N-Person Cooperative Games
8.2 Characteristic Function and Imputation
8.3 Core and Stable Set
8.4 Harold Pinter's The Caretaker
8.5 Shapley Value
8.6 Kernel, Nucleolus, and Least Core
8.7 Coalition-Predicting Theories
8.7.1 Equal Excess Theory
8.7.2 Caplow's Theory
8.7.3 Minimal Winning
Coalition Theory
8.7.4 Minimum Resource Theory
8.8 Experiments on Coalition Formation
8.9 Summary
9.
Multi-Person Non-Cooperative Games and Social Dilemmas
9.1 N-Person Non-Cooperative Games: Nash
Equilibria
9.2 The Chain-store Paradox and Backward
Induction
9.3 Auction Games and Psychological Traps
9.4 Social Dilemmas: Intuitive Background
9.4.1 The
"Invisible Hand" and Voluntary Wage Restraint
9.4.2 Conservation of
Natural Resources
9.4.3 The Tragedy of the
Commons
9.5 Formalization of Social Dilemmas
9.6 Theory of Compound Games
9.7 Empirical Research on Social Dilemmas
9.7.1 Group Size Effects
9.7.2 Communication Effects
9.7.3 Individual Differences
and Attribution Effects
9.7.4 Payoff and Incentive
Effects
9.7.5 Framing Effects
9.8 Summary
APPLICATIONS
10. Social
Choice and Strategic Voting
10.1 Background
10.2 Alternatives, Voters, Preferences
10.3 Voting Procedures
10.4 Voting Paradoxes
10.5 Arrow's Impossibility Theorem
10.6 Proportional Representation: Single Transferable
Vote
10.7 Strategic (Tactical) Voting
10.8 Sophisticated Voting
10.9 Empirical Evidence of Strategic Voting
10.10 Summary
11. Theory
of Evolution: Strategic Aspects
11.1 Historical Background
11.2 Strategic Evolution and Behavioural Ecology
11.3 Animal Conflicts and Evolutionarily Stable
Strategies
11.4 An Improved Multi-Person Game Model
11.5 Empirical Evidence
11.6 Summary
12. Game
Theory and Philosophy
12.1 Relevance of Game Theory to Practical Problems
12.2 Rationality in Games
12.2.1 Coordination games
12.2.2 Prisoner's Dilemma
games
12.3 Newcomb's Problem
12.4 Kant's Categorical Imperative
12.5 Plato, Hobbes, Rousseau: Social Contract Theories
12.6 Evolution and Stability of Moral Principles
12.7 Summary
Appendix
A Simple Proof of the Minimax Theorem
A.1 Introductory Remarks
A.2 Preliminary Formalization
A.3 The Minimax Theorem
A.4 Proof
A.5 Remark
References
Index
Preface to the Second Edition
The first edition of this book was entitled Game Theory and Experimental Games: The Study of Strategic Interaction and was published by Pergamon Press in 1982. It aimed to bridge the gap between game theory and its applications by providing an introduction to the theory and a reasonably comprehensive survey of some of its major applications and associated experimental research. Its more specific objectives were to explain the fundamental ideas of mathematical game theory from first principles and to provide an introductory survey of experimental games and other applications of the theory in social psychology, decision theory, evolutionary biology, economics, politics, sociology, operational research, and philosophy.
The first edition was favourably received and generously reviewed on both sides of the Atlantic and adopted as a text for a number of specialist courses. Demand for the book, though modest, remained remarkably steady for many years, but theoretical developments and new empirical findings accumulated over the years, making the need for a revision of the original text increasingly difficult to ignore. This second edition is so radically revised as to be hardly the same book, and I believe it to be a significant improvement on the first. The principal changes that I have introduced are as follows. I have modified the title, at the suggestion of the publisher, to indicate the scope of the book more accurately. I have corrected the errors and plugged the gaps that have been pointed out to me, and I have introduced numerous amendments and improvements to every chapter. I have thoroughly updated the contents of the book to include significant or interesting theoretical developments and empirical research findings related to coordination games, social dilemmas, strategic aspects of evolutionary biology, framing effects, strategic voting, and many other areas of research. In the light of comments from readers and reviewers I have introduced a little more formal mathematics where omitting it seems to have created more problems than it solved.
In addition, I have improved the book's coverage by incorporating into this second edition a number of important topics that have developed recently or were missing from the first edition for other reasons. Chapter 3 now includes a great deal more theoretical and empirical work on coordination games and the minimal social situation. Chapter 6 includes a section on subgame perfect and trembling-hand equilibria and a further section on bargaining solutions for two-person cooperative games; chapter 7 includes a discussion of Axelrod's tournaments of Prisoner's Dilemma game computer programs and a brief review of cross-cultural comparisons of cooperativeness; chapter 8 is renamed and largely rewritten to include a detailed review of the major theories of coalition formation; chapter 9 is renamed and restructured and includes a discussion of the Chain-store paradox and backward induction; chapter 10 is renamed and restructured and incorporates material on strategic voting, which was in a separate chapter of its own in the first edition, and a discussion (requested by a number of readers) of proportional representation voting procedures, chapter 11 is renamed and includes a refutation of the notion that the strongest always survive in evolutionary games, and chapter 12 is renamed and restructured and includes discussions of philosophical problems related to coordination games and Newcomb's problem.
I no longer believe that "ideas are almost invariably expressed more clearly and forcefully by their inventors or discoverers than by subsequent commentators", as I said in the preface to the first edition. I now believe, on the contrary, that innovators sometimes struggle to understand their own inventions or discoveries and that their successors often understand and explain them better. I have therefore been more liberal with my citations of secondary sources in this edition.
I remain indebted to the people who helped me with the first edition and were acknowledged in its preface. Preparation of this edition was facilitated by Grant No. L122251002 from the Economic and Social Research Council as part of the research programme on Economic Beliefs and Behaviour. Numerous thoughtful readers in Britain, the United States, the Netherlands, and elsewhere have made helpful suggestions that have been incorporated into this second edition, and I am grateful to them all. They are too numerous to list exhaustively, but special thanks are due to Jerome Chertkoff, whose thoughtful review in Contemporary Psychology included constructive suggestions for improvement that I have implemented fully, to Werner Tack and Manfred Vorwerg, who also offered important practical advice that I have followed, to Michael Bacharach of Oxford University and other colleagues involved in the Framing, Salience and Product Images research project for inspiration and advice, to Brian Parkinson and David Stretch, who provided useful comments, to Roy Davies, who helped me to improve the mathematical appendix and the general presentation of this edition, to Zhu Zhifang of Wuhan University in the Republic of China, who discovered an important though deeply hidden error while working on a Chinese translation of the book, and to Kathy Smith for preparing many of the payoff matrices. But in spite of everyone's help and my own best efforts, this book is not free of errors. It cannot be error-free, because if it were, then the sentence immediately preceding this one would be an error, which would mean that it was not error-free after all. I should be grateful to readers who spot any more serious defects or who have any other comments to make.
Andrew M. Colman