Introduction to the Series
(International Series in Experimental Social Psychology)
Michael Argyle
Social psychology is in a very interesting period, and one of rapid development. It has survived a number of "crises", there is increased concern with external validity and relevance to the real world, the repertoire of research methods and statistical procedures has been greatly extended, and a number of exciting new ideas and approaches are being tried out.
The books in this series present some of these new developments; each volume contains a balance of new material and a critical review of the relevant literature. The new material consists of empirical research, research procedures, theoretical formulations, or a combination of these. Authors have been asked to review and evaluate the often very extensive past literature, and to explain their new findings, methods or theories clearly.
The authors are from all over the world, and have been very carefully chosen, mainly on the basis of their previous published work, showing the importance and originality of their contribution, and their ability to present it clearly. Some of these books report a programme of research by one individual or a team, some are based on doctoral theses, others on conferences.
Social psychologists have moved into an increasing number of applied fields, and a growing number of practitioners have made use of our work. All the books in this series will have some practical application, some will be on topics of wide popular interest, as well as adding to scientific knowledge. The books in the series are designed for advanced undergraduates, graduate students and relevant practitioners, and in some cases for a rather broader public.
We do not know how social psychology will develop, and it takes quite a variety of forms already. However, it is a great pleasure to be associated with books by some of those social psychologists who are developing the subject in such interesting ways.
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Preface
The primary aim of this book is to provide a critical survey of the essential ideas of game theory and the findings of experimental research on strategic interaction. In addition, I have reported some new experiments using lifelike simulations of familiar kinds of strategic interactions, and included discussions of recent applications of game theory to the study of voting, the theory of evolution, and moral philosophy. The time has (alas) long since passed when a single person could reasonably hope to be an expert on all branches of game theory or on all of its applications, and I have not achieved the impossible. But I thought it worthwhile, nonetheless, to aim for a fairly comprehensive coverage of important topics, with particular emphasis on those which seem to be most relevant to naturally occurring strategic interactions.
Game theory and the experimental gaming tradition have grown up in relative isolation from each other. Game theorists, in general, remain largely oblivious of the empirical studies that have been inspired by the theory, and experimental investigators have tended to assume that the nuts and bolts of the theory do not concern them. Both parties are the losers from this divorce, and I have therefore tried to contribute towards a reconciliation by examining in detail, for the first time in a single volume, both sides of the story.
My goal has been to introduce and evaluate the fundamental theoretical ideas, empirical findings, and applications as clearly as possible without over-simplifying or side-stepping important difficulties. In so far as I have succeeded, this is the kind of book I should have liked to have read when I first became interested in game theory and experimental games, or better still, before I had developed any interest in these matters. Wherever possible, I have attributed seminal contributions to their originators and cited the original sources: ideas are almost invariably expressed more clearly and forcefully by their inventors or discoverers than by subsequent commentators. But I have also cited many useful review articles which will be of assistance to readers wishing to pursue particular topics in depth.
The most important chapters for social psychologists and others whose primary interest is in such strategic phenomena as cooperation, competition, collective equilibria, self-defeating effects of individual rationality, coalition formation, threats, altruism, spite, escalation, social entrapment, and so forth, are Chapters 1,2, 3, 6, 7, 8, and 9. Mathematically inclined readers should pay special attention to Chapters 4, 8,10, and 11, and to Appendix A in which the minimax theorem is rigorously proved. The chapters which are most relevant to sociology, economics, and politics are Chapters 1, 2, 6, 8, 10, and 11. Biological applications are discussed in Chapter 12, but Chapters 1, 2, 6, and 8 provide a necessary background to it. Philosophical applications are dealt with primarily in Chapter 13, to which Chapters 1,2,6, 8, and 12 provide the necessary background. Most of the translations from original French and German sources in Chapter 13 and elsewhere are my own.
I am indebted to a number of people who contributed to this book in various indirect ways. In particular, I am grateful to Michael Argyle, Alan Baker, Barbara Barrett, Dorothy Brydges, Roy Davies, Julia Gibbs, Gabriele Griffin, John Lazarus, Nicholas Measor, Richard Niemi, Ian Pountney, Albert W. Tucker, Diane Williams, Bill Williamson, and the Research Board of the University of Leicester. I should be delighted to receive comments from readers, indicating their reactions to the final product.
Andrew M. Colman
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Contents
BACKGROUND
1 Introduction
1.1 Intuitive Background 3
1.2 Abstract Models: Basic Terminology 5
1.3 Skill, Chance, and Strategy 9
1.4 Historical Background 11
1.5 Summary 13
2 One-Person Games
2.1 Games Against Nature 14
2.2 Certainty 14
2.3 Risk 16
2.4 Utility Theory 18
2.5 Uncertainty 22
2.6 Summary 30
3 Pure Coordination Games and the Minimal Social Situation
3.1 Strategic Collaboration 31
3.2 Pure Coordination Games 31
3.3 The Minimal Social Situation 37
3.4 Summary 44
THEORY AND EMPIRICAL EVIDENCE
4 Two-Person, Zero-Sum Games
4.1 Strictly Competitive Games 47
4.2 Extensive and Normal Forms 48
4.3 Games With Saddle-Points 51
4.4 Games Without Saddle-Points 54
4.5 Dominance and Admissibility 61
4.6 Methods for Finding Solutions 63
4.7 Ordinal Payoffs and Incomplete Information 68
4.8 Summary 73
5 Experiments With Strictly Competitive Games
5.1 Ideas Behind Experimental Games 74
5.2 Review of Research on Non-Saddle-Point Games 76
5.3 Review of Research on Saddle-Point Games 80
5.4 Critique of Experimental Gaming 82
5.5 Experiment I: Abstract and Lifelike Strictly Competitive Games 85
5.6 Summary 92
6 Two-Person, Mixed-Motive Games: Informal Game Theory
6.1 Mixed-Motive Games 93
6.2 Classification of 2 x 2 Mixed-Motive Games 94
6.3 Leader 95
6.4 Battle of the Sexes 97
6.5 Chicken 98
6.6 Prisoner's Dilemma 101
6.7 Comparison of the Archetypal 2 x 2 Games 105
6.8 Metagame Theory 107
6.9 Summary 112
7 Experiments With Prisoner's Dilemma and Related Games
7.1 The Experimental Gaming Literature 113
7.2 Strategic Structure 114
7.3 Payoffs and Incentives 118
7.4 Circumstances of Play 119
7.5 Responses to Programmed Strategies 123
7.6 Sex Differences 124
7.7 Attribution Effects 126
7.8 Investigations of Ecological Validity 128
7.9 Experiment II: Abstract and Lifelike Prisoner's Dilemma Games 131
7.10 Experiment III: Abstract and Lifelike Chicken Games 136
7.11 Summary 140
8 Multi-Person Games: Social Dilemmas
8.1 Multi-Person Game Theory 142
8.2 Non-Cooperative Games: Equilibrium Points 144
8.3 Cooperative Games: Characteristic Functions 145
8.4 Harold Pinter's "The Caretaker" 149
8.5 The Shapley Value 151
8.6 The Dollar Auction Game and the Concorde Fallacy 153
8.7 Multi-Person Prisoner's Dilemma 156
8.8 General Theory of Compound Games 163
8.9 Summary 166
9 Experiments with Coalition, Auction, & Social Dilemma Games
9.1 Multi-Person Experimental Games 168
9.2 Coalition Formation 169
9.3 Auction Games and Psychological Traps 173
9.4 N-Person Prisoner's Dilemma 178
9.5 Experiment IV: Abstract and Lifelike N-Person Prisoner's Dilemmas 184
9.6 Summary 190
APPLICATIONS
10 Sincere Voting and Collective Choice Theory
10.1 Background 195
10.2 Alternatives, Voters, Preferences 196
10.3 Axioms Concerning Individual Preferences 197
10.4 Voting Procedures 198
10.5 Condorcet's Paradox 201
10.6 Probabilities of Cyclic Majorities 204
10.7 Arrow's Impossibility Theorem 207
10.8 The Borda Effect 210
10.9 Summary 213
11 Strategic Voting
11.1 Optimal Voting Strategies 214
11.2 Historical B ackgr ound 215
11.3 Insincere Voting and Equilibrium Points 215
11.4 The Classical Solution: Dominance and Admissibility 219
11.5 Sophisticated Voting 222
11.6 Anticipated Decisions and Multistage Solutions 224
11.7 General Results on Strategic Voting 228
11.8 Is Strategic Voting Unfair? 231
11.9 Empirical Evidence 233
11.10 Summary 234
12 Theory of Evolution: Strategic Aspects
12.1 Historical Background 235
12.2 Strategic Evolution 235
12.3 Animal Conflicts and Evolutionarily Stable Strategies 238
12.4 An Improved Multi-Person Game Model 243
12.5 Empirical Evidence 250
12.6 Summary 253
13 Moral Philosophy and Practical Problems of Strategy
13.1 Game Theory and the Conduct of Life 254
13.2 Rationality and Self-interest 257
13.3 Kant's Categorical Imperative 262
13.4 Rousseau's Social Contract 264
13.5 Evolution and Stability of Moral Principles 266
13.6 Summary 268
Appendix A: A Simple Proof of the Minimax Theorem
A.1 Introductory Remarks 273
A.2 Preliminary Formalization 273
A.3 The Minimax Theorem 274
A.4 Proof 275
References 281
Index
