The diversity of sameness

288 Pages·1998·89.626 MB·English

by  László Mérő

Moral
Calculations
Game Theory, Logic,
and Human Frailty
Laszlo Mera
Translated by Anna C. Gosi-Greguss
English Version Edited by David Kramer
c
COPERNICUS
An Imprint of Springer-Verlag
Illustrations by Mikl6s M. Miltenyi.
© 1998 Springer-Verlag New York, Inc.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,
or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording,
or otherwise, without the prior written permission of the publisher.
Published in the United States by Copernicus, an imprint of Springer-Verlag New York, Inc.
Copernicus
Springer-Verlag New York, Inc.
175 Fifth Avenue
New York, NY lOOlO
USA
Library of Congress Cataloging-in-Publication Data
Mer6, Uszl6.
Moral calculations: game theory, logic, and human frailty /
Uszl6 Mer6.
p. cm.
"Copernicus imprint."
Includes bibliographical references and index.
ISBN 0-387-98419-4 (hardcover: alk. paper)
1. Game theory. 2. Thought and thinking. 1. Title.
QA269.M457 1998
519.3-DC21 98-17443
Manufactured in the United States of America.
Printed on acid-free paper.
9 8 7 6 543 2
ISBN 0-387-98419-4 SPIN lO659411
Preface
This book is about rational thinking-something that may, perhaps,
not even exist. There are many indicators that human thinking is es
sentially nonrational, even in those cases where the methods of pure
logic can effectively be applied. I addressed this matter in my book
Ways of Thinking. The present book does not rely on Ways of
Thinking, but rather complements it: Here we are going to discuss
thinking from the point of view of John von Neumann's theory of
games.
I shall not attempt to characterize the mathematical level of this
book, because it has none. Here you will find no formulas whatso
ever, although you will occasionally meet ideas whose origins are
mathematical. To understand the book you will need no mathemat
ics beyond the four basic arithmetical operations. Nevertheless, I do
not promise the reader an easy time of it, and I defend myself with
the words of Frigyes Karinthy, the father of Hungarian satire: "It's not
me that's complicated; what's complicated is what I'm talking about."
This book is in the form of an essay. It is intended primarily to be
read rather than studied, although parts of it could be taught in a
university course. Therefore, I did not stick to the fundamental rules
of textbook wri~ti ng, namely, that the material be easy to learn, easy to
teach, and easy to examine on-usually at the expense of being
slightly boring. Rather, my aim was to meet the demands of the
reader seeking mental adventure. Nevertheless, I found it useful to
differentiate between generally accepted scientific theories and facts
on the one hand, and my own views on the other. For the former I
use the first person plural or passive voice, while for the latter I em
ploy the first person Singular. Although even what is presented as
vi Preface
science should not be viewed as indisputable, I definitely hope that
my opinions will provoke debate and further thought.
The book is divided into three parts. The first part introduces the
basic concepts of game theory, together with several games and real
life situations that illustrate the theory's ideas and typical approaches
to different psychological and moral issues. The second part is prob
ably the most difficult of the three. Here I demonstrate in five differ
ent fields of science-mathematics, psycho loW' evolutionary biol
ogy, economics, and quantum physics-the diversity of ways in
which the ideas of game theory can manifest themselves. In the third
part the lines converge. This part is purely about psychology-about
rational thinking in particular-which is not at all the same as logi
cal thinking.
I would like to thank Csaba Andor, Laszlo Antal, Eva Banyai,
Miklos Barabas, Nora Bede, Aniko Bodi, judit Bokor, Ferenc Brody,
Zsuzsa Csanyi, Istvan Czigler, Andrea Dull, Peter Futo, Eva Gartner,
Csilla Greguss, janos Herczeg, Monika HoIcsa, Gyorgyi Hosszu,
Sandor Illyes, Andras joo, Zsuzsa Kaldy, Ildik6 Kiraly, Erika Kovacs,
Eva Kovacshcizy, Kriszta Mady, Csaba Mer6, Katalin Mer6, Vera
Mer6, Nora Nadasdy, Balazs Nagy, janos Pataki, Ferenc Pinter, julia
Seb6, Istvan Siklosi, Endre Somos, Dora Speer, Eszter Szabo, judit
Szabo, Peter Tatray, Enik6 Tegyi, Robert Urban, Zoltan Olkei, Tibor
Vamos, Katalin Varga, Zoltan Vassy, and Zsuzsa Votisky for their
ideas, remarks, suggestions, and criticism. The preparation of this
book was generously supported by grant No. T-006845 from aTKA
to the author.
Laszlo Mer6
Budapest, Hungary
Contents
Preface v
Games of Morality 1
1. Auction and Posing 3
The Dollar Auction Game 3
The Three Critical Points 4
Out of the Party and into the Psych Lab 5
High-Stakes Auctions 8
Dollar Auctions in Everyday Life 9
Dollar Auctions in the Wild 10
Posing for a Random Period 12
2. The Brute as Hero 15
Dice and the Common Interest 17
A Martian Humankind 19
The Protagonist Appears 20
Game Theory 21
Pure and Mixed Strategies 23
Optimal Mixed Strategies 25
Who Optimizes~ and Why? 26
3. The Prisoner's Dilemma 28
Two Logical Solutions 29
On the Nature of Logic 31
Everyday Prisoner's Dilemmas 32
Prisoner's Dilemmas with Many Persons 36
Iterated Prisoner's Dilemmas 37
viii Contents
Axelrod's Competitions 39
The Personality Traits of the Programs 40
Tit for Tat in Sticklebacks 43
Psychological Experiments with the Prisoner's Dilemma 44
The Significance of Phrasing 46
4. The Golden Rule 48
Logic and the Golden Rule 49
The Categorical Imperative 51
t>
The Categorical Imperative and Diversity 53
The Gift of the Magi 55
The Basic Forms of Two-Person Games with Mixed Motivation 58
Chicken 60
Asymmetric Games 62
The Dollar Auction and Ethical Principles 63
Cooperation and Rationality 65
5. The Bluff 67
The World of Poker 69
A Simple Poker Model 70
The Evolution of the Poker Face 72
The Poker Model Analyzed 73
Bluff Big or Not at All 76
Bluff as a Cognitive Strategy 77
Nature's Bluffs 78
The Sources of Diversity 81
6. John von Neumann's Game Theory 83
The Case of the Schizophrenic Snail 84
The Mathematical Background of von Neumann's Theorem 87
The Principle of Rationality 88
Rational Players 89
The Value of the Game 91
Stone-Paper-Scissors 92
Generalizations of von Neumann's Theorem 95
Games with Handicap 98
The Part and the Whole 100
Contents ix
7. Competition for a Common Goal 103
Purely Cooperative Games 104
Mutual Fate Control 107
Theoretical Considerations 108
Experimental Evidence 110
Asynchronous Decisions 111
The Role of Being Informed 113
The Rationale of Curfews 114
On the Nature of Psychological Laws 116
Cooperation by Competition 117
8. Hawks and Doves 119
The Theory of Group Selection 121
The Theory of Gene Selection 123
Competition Between the Two Theories 125
The Struggle Between Hawks and Doves 127
Rationality in the Selfish Gene Theory 129
Rationality in Group Selection Theory 130
Complex Strategies 132
9. Socialism and Free Enterprise 135
Economics and Evolution 136
The Invisible Hand 138
Theories of EqUilibrium 140
Planned Economies 142
The Diversity of Mixed Economies 145
The Logic of Evolution 147
10. Games Elementary Particles Play 150
The Dual Nature of Light 152
Two-Slit Experiments 155
If You Ask a Stupid Question .. . 157
Schr6dinger's Equation 159
Probabilistic Frogs 160
Chance as an Organizing Force 163
Searching for the Grand Unified Theory 166
The Great Game of Nature 169
Contents
The Psychology of Rationality 173
11. Loves Me, Loves Me Not ... 175
Schrodinger's Cat 176
Digression: "Poetic" Thoughts 178
The Contingency of Human Concepts 180
Stone-Paper-Scissors Redux 182
The Cheating Innkeeper 183
Quasi-rationality 185
Plucking Petals 186
Distancing 189
12. Rational Irrationality 191
Correct Decisions Reached by Inadequate Methods 192
Fortuities of Consciousness 194
The Methods of Rational Decisions 196
Meditative Techniques 198
The Scientific Foundations of Meditative Techniques 201
Ideomotor Techniques 202
Today Thus, Tomorrow Otherwise 203
Logic and Intuition 205
13. Collective Rationality 208
Analysis of the Science 84 Game 210
Outcome of the Million Dollar Game 212
The Hidden Aim of the Game 214
The Hiding Lottery 216
The Smallest Number Wins Game 219
The Means of Collective Rationality 222
14. The Heterogeneity of Human Thought 225
Logically Isomorphic Tasks 227
On the Role of Rationality 229
Descartes's Error 231
Where Does Rationality Reside in Us? 234
Games People Play 237
Further Aspects of Games 240
15. There Are Many Ways to Nirvana 242
The Nature of Rational Cognition 244
The Nature of Mystical Cognition 246
Contents xi
Rationality as a Technique of Distancing 249
Beyond Rationality 251
The Two Components of Thinking 253
Game as Essence 254
Nirvana 256
References and Further Reading 261
Index 269