Table Of ContentDECISION THEORY AND DECISION BEHAV IOUR
Also by Anatol Rapoport
SCIENCE AND THE GOALS OF MAN
OPERA TIONAL PHILOSOPHY
FIGHTS, GAMES, AND DEBATES
STRATEGY AND CONSCIENCE
PRISONER'S DILEMMA (with A.M. Chammah)
TWO-PERSON GAME THEORY
N-PERSON GAME THEORY
THE BIG TWO
CONFLICT IN MAN-MADE ENVIRONMENT
SEMANTICS
THE 2 X 2 GAME (with M. Geyer and D. Gordon)
MATHEMAT ICAL METHODS IN THE SOCIAL AND BEHA VIORAL
SCIENCES
GENERAL SYSTEM THEORY
THE ORIGINS OF VIOLENCE
CANADA AND THE WORLD (with Anthony Rapoport)
PEACE, AN IDEA WHOSE TIME HAS COME
Decision Theory and
Decision Behaviour
Second Revised Edition
Anatol Rapoport
© Anatol Rapoport 1989, 1998
Softcover reprint ofthe hardcover 2nd edition 1998978-0-333-68147-3
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identified as the author of this work in accordance
with the Copyright, Designs and Patents Act 1988.
First edition (Kluwer) 1989
Second edition (Macmillan) 1998
Published by
MACMILLAN PRESS L TD
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and London
Companies and representatives
throughout the world
ISBN 978-1-349-39988-8 ISBN 978-0-230-37776-9 (eBook)
DOI 10.1057/9780230377769
A catalogue record for this book is available
from the British Library.
This book is printed on paper suitable for recycling
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10 9 8 7 6 5 4 3 2
07 06 05 04 03 02 01 00 99 98
Contents
Preface to the First Edition xi
Preface to the Second Revised Edition xv
Acknowledgements xvii
PART I DECISIONS INVOLVING A SINGLE ACTOR
Introduction: An Overview of Decision Theory 3
Branches of decision theory 4
Multi-objective decision problems 6
Social choice as a multi-objective decision problem 7
Descriptive decision theory 7
1 Orders and Scales 10
Binary relations 10
Orders induced by a preference relation 11
Utilities determined on a ratio sc ale 17
Construction of a ratio sc ale of preference 19
Empirical determination of the utility function 21
2 Optimization 26
Linear programming 30
The simplex method 34
The primal and the dual 39
The general optimization problem 42
Dynamic programming 46
3 Decisions under Uncertainty and Risk 50
The principle of insufficient reason 50
The maximin principle 51
The maximax 51
The Hurwicz-a 52
Minimax regret 52
Criteria to be satisfied by adecision rule 53
Some aspects of behaviour in decision situations under uncertainty 57
The ElIsberg paradoxes 60
Decisions under risk 62
Expected gain and expected utility 64
Value of information 66
The three condemned men 67
Cost-benefit analysis of information acquisition 68
Statistical decisions 74
v
vi Contents
The value and limitations of mathematical models in theories of
decision under risk 80
4 Subjective Aspects of Risk 82
Misconceptions about risk 89
Assessment of subjective probabilities 97
Pejorative connotations of risk 100
5 Modifications and Generalizations of Expected Utility Theory 105
Theory of prospects 108
Regret in decision-making 118
Generalized expected utility analysis 123
Experimental test of the generalized utility model 130
Is generalization of EU an extension of rationality? 133
6 Multi-objective Decisions 136
Expected utility and additivity 143
Experimental test of SEU, SEV, EU and EV theories 144
Lexicographic ordering 148
An application of the EBA model 153
The matching problem 156
7 Theory of Social Choice 160
Axiomatization of desiderata of a social choice function 161
The liberalism paradox 168
Alternative approaches to the problem of social choice 170
Condorcet functions 171
8 Individual Psychology of Decision-making 174
Cognitive dissonance 178
Cognitive balance 180
Conflict decision theory as an extension of cognitive dissonance 181
Limitations of freedom of choice 183
PART 11 NON-COOPERATIVE GAMES
9 Two-person Constant Sum Games 189
Solving two-person zero sum games by the simplex method 197
Intuitive approaches to solutions of two-person constant sum games 201
The theoretical importance of two-person constant sum games 206
10 Some Topics in Continuous Games 208
Games of timing 208
Differential games 214
Some interesting examples of differential games 222
Contents vii
11 Two-person Non-constant Sum Games 226
What is the most 'rational' outcome? 230
Payoff dominance and risk dominance 231
Stability 232
Perfectness 234
A taxonomy of 2 X 2 games 238
Types of experiments with 2 X 2 games 240
Comparisons of performances in iterated chicken and prisoner's
dilemma 241
Top dog-underdog 242
Benevolence and trust 246
Opposite pressures in prisoner's dilemma 249
The effect of others' strategy in iterated prisoner's dilemma 250
Psychological pressures in a 'top dog-underdog' game 251
Non-monotonie pressures in chicken 252
12 Social Dilemmas 254
Independent and interdependent maximization 254
Parasitism and Symbiosis 256
Game models of social dilemmas 257
Public goods and private interest 258
Generalized prisoner' s dilemma 259
Two paradoxes of backward induction 260
The chain store paradox 261
Tragedy of the commons 262
Volunteer's dilemma 263
Groups-size effects in n-person social traps 266
The Platonia dilemma 268
The largest number game 271
13 Applications of Game Theory in Biology 273
Evolutionary games 274
A timing game with a unique ESS 277
Evolutionary dynamics 279
Simulating the evolution of cooperation 281
A simulation experiment with human subjects 283
Reputation effects 286
The blurred boundary between competition and cooperation 290
14 Theory of V oting 297
Voting strategies 301
The case of the unqualified librarian 304
Sophisticated voting 306
The chairman paradoxes 308
viii Contents
PART III COLLECTIVE DECISIONS
15 Two-person Cooperative Games 315
Zeuthen's model of bargaining 320
Nash's solution of the two-person cooperative game 321
The individualistic orientation in Nash's solution 324
Experiments with 2 X 2 cooperative games 325
Other approaches to solutions of cooperative games 332
16 N-person Cooperative Games 337
Stahle sets 341
The Shapley Value 343
Comparison of the stable set, the Shapley Value and the core 345
The nucleolus 346
Comparison of the four solutions of the small market game 348
Rationales for the various solution concepts 351
17 The Allocation Problem 354
Game-theoretic approaches to the allocation problem 355
Tests of game-theoretic solutions of allocation problems 357
Allocation of aircraft landing fees 362
18 Indices of Power 366
Power of political coalitions 367
The problem of choosing an index of power 371
External validity of power indices 372
Power and satisfaction 374
The case for proportional representation in electoral systems 378
19 Theories of Coalition Formation 383
Experiments in coalition formation 384
Formation ofpolitical coalitions 387
A game-theoretic approach to formation of political coalitions 388
20 Game-theoretical Concepts in Economics 394
Allocation of resources in a competitive economy 394
The Edgeworth market 398
Generalized coalition structure: 'leaks in the cliques' 405
Games and markets that generate them 408
The problem of reductionism: can a macroworld be derived from a
microworld? 411
Utility of theories 415
The emergence of institutions 416
Contents ix
21 Psychology of Collective Decision-making 418
Amplification of probabilistic preference 419
The 'risky-shift' effect 422
Quality of group decisions in real life situations of momentous
import 426
Concluding Remarks 434
Glossary of Symbols and Terms 441
Notes 446
References 451
Name Index 459
Subject Index 462
