Essays on Information Acquisition
Essays on Information Acquisition
Jun Chen
Dissertation for the Degree of Doctor of Philosophy, Ph.D.,
in Economics
Stockholm School of Economics, 2016
Essays on Information Acquisition
c SSE and Jun Chen, 2016
ISBN 978-91-7731-002-0 (printed)
ISBN 978-91-7731-003-7 (pdf)
This book was typeset by Jun Chen using LATEX.
Printed by:
Ineko, Göteborg, 2016
Keywords:
Information acquisition, global games, uncertainty, committee decision,
competition, monopoly, public information, transparency, endogeneity.
iii
To my family
Foreword
This volume is the result of a research project carried out at the Department
of Economics at the Stockholm School of Economics (SSE).
This volume is submitted as a doctor’s thesis at SSE. In keeping with the
policies of SSE, the author has been entirely free to conduct and present his
research in the manner of his choosing as an expression of his own ideas.
SSE is grateful for the financial support provided by the Jan Wallander and
Tom Hedelius Foundation which has made it possible to fulfill the project.
Göran Lindqvist
Richard Friberg
Director of Research
Stockholm School of Economics
Professor and Head of the
Department of Economics
Stockholm School of Economics
Acknowledgements
Before and during my PhD I had the fortune to know and meet many people
who helped me a lot in the ongoing studies and researches. I am grateful to all
of them.
First and foremost, I am deeply indebted to my supervisor Jörgen Weibull
for his precious advice and endless encouragement throughout my PhD. I could
not have imagined a better supervisor and mentor for my PhD study. His enthusiasm for economics and his detailed suggestions helped me in all the time of
research and writing of this thesis. Many meetings with him were continuing
sources of inspiration in these years. In addition he inspired me to communicate with others about research ideas and this really helped me a lot.
My sincere thanks also goes to Mark Voorneveld for his insightful comments. Especially his suggestion on the last chapter has helped me a lot in
organizing and improving that paper.
I would not have started a PhD without the support and encouragement
from my master supervisor Yanbin Chen. Yanbin helped me open the gate to
economic research and showed me the satisfaction of research and its potential.
He aroused my interest in economic research and convinced me of pursuing a
PhD.
I would also like to take the opportunity to thank other faculties and PhD
students at Stockholm School of Economics. I greatly benefited from the insightful comments of Richard Friberg, Tore Ellingsen, Lars Ljungqvist and
Erik Lindqvist during the lunch seminars. I also had the honor to know the
English professors Thomas Lavelle and Alan Shima, they were very helpful
in improving my English. I also thank the comments from Arieda Mucq and
Markus Sigonius. It’s my great honor to share the office with Markus during the whole PhD study. He was a good officemate: he had made my life in
Stockholm much more convenient; we also had many discussions from the life
amenities to economic research.
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ESSAYS ON INFORMATION ACQUISITION
I am grateful to the administrative staffs at Stockholm School of Economics.
Ritva Kiviharju, Idha Hobro, Pia Ylinen and Camilla Elwing-Johansson had
helped me many times in the school during these years. I also thank Camilla for
showing me Stockholm and letting me have the opportunity to know the city
better. I am also very grateful for the financial support from Knut and Alice
Wallenberg Research Foundation, and the support from Paul Segerstrom.
It’s very good to have friends each time when I went back home. Thank
Liujian Yang for his arrangement for my living and traveling in Shanghai. It
was also very good to share the happiness with Zhibin Yi, Fuqing Huang and
Yiping Ouyang. It was also helpful to discuss economic research ideas with
Jinchao Yi. During these years I sometimes felt depressed and it was nice for
me to get the comfort from my old friends in China.
Last, but certainly not the least, I would like to thank my family: my parents, my aunts and uncles, my brothers and sisters and especially my grandparents for supporting me spiritually throughout the PhD. study and my life in
general.
Stockholm, July 2016
Jun Chen
Contents
Introduction
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1
Information and Multiplicity in Global Games: A Survey
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Benchmark: Exogenous Information . . . . . . . . . . . .
1.3 Endogenous Public Information . . . . . . . . . . . . . .
1.3.1 Price In Trade . . . . . . . . . . . . . . . . . . . .
1.3.2 Observing Each Other . . . . . . . . . . . . . . .
1.4 Endogenous Private Information . . . . . . . . . . . . . .
1.4.1 Wait and Delay in Global Games . . . . . . . . .
1.4.2 Rigid Information Acquisition in Global Games .
1.4.3 Flexible Information Acquisition in Global Games
1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . .
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REFERENCES
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The Condorcet Jury Theorem with Information Acquisition
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 The First-best Solution . . . . . . . . . . . . . . . . . . .
2.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Committee Size and Social Welfare . . . . . . . . . . . . .
2.5.1 Rational Ignorance . . . . . . . . . . . . . . . . .
2.5.2 The asymptotic results . . . . . . . . . . . . . . .
2.6 A Priori Imbalance . . . . . . . . . . . . . . . . . . . . .
2.7 Extension . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . .
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Appendices
2.A Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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REFERENCES
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3
Private versus Public Monopoly
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Unregulated profit maximization . . . . . . . . . . . . . . . .
3.4 First best . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Intermediate cases . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Second-best: budget-constrained welfare maximization
3.6 Numerical simulations . . . . . . . . . . . . . . . . . . . . .
3.6.1 Profit maximization . . . . . . . . . . . . . . . . . .
3.6.2 First best . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Second-best . . . . . . . . . . . . . . . . . . . . . . .
3.7 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . .
REFERENCES
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Competition and Costly Information Acquisition in Oligopoly Markets
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4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.1.1 Related Literature . . . . . . . . . . . . . . . . . . . 147
4.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
4.4 Industry Profit . . . . . . . . . . . . . . . . . . . . . . . . . 165
4.4.1 Efficient Information Acquisition for the Industry . . 165
4.4.2 Public Information . . . . . . . . . . . . . . . . . . . 167
4.4.3 Market Competition . . . . . . . . . . . . . . . . . . 170
4.5 Social Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . 174
4.5.1 Efficient Information Acquisition for the Society . . . 174
4.5.2 Public Information . . . . . . . . . . . . . . . . . . . 183
4.5.3 Market Competition . . . . . . . . . . . . . . . . . . 186
4.6 Linear Information Acquisition Cost Function . . . . . . . . 190
4.6.1 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 191
CONTENTS
4.7
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4.6.2 Industry Profit . . . . . . . . . . . . . . . . . . . . . 192
4.6.3 Social Welfare . . . . . . . . . . . . . . . . . . . . . . 194
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Appendices
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4.A Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
4.B Efficient Information Acquisition under Efficient Use . . . . 223
REFERENCES
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Introduction
This dissertation consists of four self-contained chapters that explore agent’s
information acquisition and the effects of this endogeneity of private information. The first chapter shows the importance of information structures in
global games, one of the important information structure is when agent’s private information is endogenous. The second paper studies the information
acquisition in a committee decision problem and shows how the endogeneity of private information affects the Condorcet Jury Theorem. The third
and fourth paper study firm’s behavior when their private information is endogenous. The third paper studies what affects the monopolist’s private information acquisition in equilibrium in a model where the monopolist does
not know consumers’ tastes. The fourth chapter studies the effects of public
information and market competition on private information acquisition in a
Cournot market where each firm does not know the intercept of the inverse
demand function.
In the first chapter I survey the development of information structures in
global games and study the conditions for uniqueness and multiplicity of equilibria in different information structures. In global games with exogenous information uncertainty in signals will produce uncertainty in higher-order beliefs and this higher-order beliefs may lead to the unique equilibrium; therefore
when the private information is precise enough while the public information
is noisy enough the global games have a unique equilibrium. However when
the public information is endogenous, more precise private information will
increase the precision of public information, which further lead to little uncertainty in the higher-order beliefs; therefore when the private information
is precise enough the global games have multiple equilibria. On the contrary,
when the public information is exogenous while the private information is endogenous and agents can only determine the quantitative nature of signals, the
precision of the public information will crowd out the private information in
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ESSAYS ON INFORMATION ACQUISITION
equilibrium and this will further affect the condition for equilibria multiplicity. However, if the public information is exogenous and agents can decide both
the quantitative and the qualitative nature of signals, there are always infinitely
many equilibria.
The second chapter analyzes a committee decision in which individuals
with common preference are uncertain which of two alternatives is better for
them. Members can acquire costly information. We show that the equilibrium is consistent with Down’s rational ignorance hypothesis that each member acquires less private information in larger committees. However, larger
committees can gather more aggregate information in equilibrium since there
are more members. The aggregate information is infinite with the size going
to infinity if and only if the marginal cost at ”zero information acquisition”
is zero. When the marginal cost at ”zero information acquisition” is positive,
the probability of making the right decision tends to be less than one when the
size of committees goes to infinity.
The third chapter is joint work with Jörgen Weibull. In this chapter we
compare private and public monopoly with how much resource they spend
on finding out what product varieties consumers want. To do this we propose a simple model in which a monopolist supplies one variety of a good;
this variety is chosen by the monopolist and consumers differ in their valuations of the good and preferences over product varieties. The monopolist
does not know the preference distribution, but can, at a cost, acquire more
or less precise information about this distribution. We analyze the monopolist’s endogenous information acquisition and choice of product variety in the
following three scenarios: an unregulated profit-maximizing monopolist, the
first-best welfare solution, a monopolist who maximizes a convex combination of profit and welfare. We also show that the last scenario is equivalent to
a welfare-maximizing monopolist facing a budget constraint. Our main finding is that, broadly speaking, whether public monopoly or private monopoly
acquires more information is determined by the distribution of the valuation,
which is mainly determined by the income and/or wealth distribution. Specifically public monopoly is preferable in societies with a wide spread in income
and/or wealth while private monopoly is better in societies with less inequality.
The fourth chapter studies the costly information acquisition and its effect
in a Cournot market with demand uncertainty. In this model firms know lit-
INTRODUCTION
3
tle about the intercept of inverse demand function, but they receive some public information and furthermore, can, at a cost, acquire private information.
First of all, I identify the crowding-out effects of market competition and public information on costly information acquisition in equilibrium; the intensity
of the two crowding-out effects depend on the precision of public information and the convexity of information acquisition cost function. I then relate
both the industry and social (in)efficiency of information acquisition to the
use of private information and explain why the efficiency in the use of private
information is no guarantee of efficiency in the private information acquisition. Next we show the effects of endogenous response in private information
on the industry/social value of market competition and public information.
Our main finding is that, when the private information is endogenous, market
transparency and the market competition can affect the magnitude, and sometimes even the sign, of the industry/social value of market competition and
public information.