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Unawareness and Contracts
Inauguraldissertation
eines Doktors der Wirtschaftswissenschaften
der Universit at Mannheim
vorgelegt von
Xiaojian Zhao
Mannheim 2010Abteilungssprecher: Prof. Tom Krebs, PhD
Referent: Prof. Dr. Ernst-Ludwig von Thadden
Korreferent: Prof. Dr. Martin Peitz
Tag der mundlic hen Prufung: 25nd March 2010
iiAcknowledgments
I am greatly indebted to my supervisor Ernst-Ludwig von Thadden for his invaluable
guidance throughout my doctoral studies. I would like to thank his continuous advice
on my research projects. His vision supported me in each crucial step in my academic
development. Without him, I could not imagine how my life would be. I am also very
grateful to Jean Tirole for his local supervision and hospitality in Toulouse school of
economics. He enhanced my courage to pursue my dreams in the intellectual world,
especially in social sciences.
I express my gratitude to my coauthors, Ying-Ju Chen in UC Berkeley, Roberta Dessi
and Sanxi Li in Toulouse school of economics, and Martin Peitz and Ernst-Ludwig von
Thadden in University of Mannheim. My research output is a result of collective e orts
and would not exist without their talent and generosity.
I thank our doctoral program in economics (CDSE) and the European Network for
Training in Economic Research (ENTER) for providing me a large number of opportu-
nities of conferences, seminars, summer schools and visits. Financial support from the
German Science Foundation (DFG) is gratefully acknowledged.
Furthermore, I bene ted substantially from discussions with some other colleagues in
University of Mannheim, University College London, Toulouse school of economics, etc.
In particular, I am grateful to Syngjoo Choi, Kim-Sau Chung, Johannes Koenen, Patrick
Rey, Burkhard Schipper, Heiner Schumacher, Rani Spiegler, and especially Jidong Zhou.
Lastly, my wife Qianying Chen provided invaluable support, understanding and love in
my life in Europe.
iiiContents
1 Introduction 1
2 Foundations of Unawareness 5
2.1 Epistemic Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Unawareness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Decision-Theoretic Foundations . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 (Bounded) Rationality . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Decision under Unforeseen Contingencies . . . . . . . . . . . . . . 15
3 Unforeseen Contingencies and Incomplete Contracts 21
3.1 Completely Unforeseen Contingencies . . . . . . . . . . . . . . . . . . . . 24
3.1.1 Information Disclosure and Consumer Awareness . . . . . . . . . 24
3.1.2 Forward Induction and Games with Strategic Announcement . . . 38
3.1.3 Forward and Insurance Contracts . . . . . . . . . . . . 40
3.2 Partially Unforeseen Contingencies . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Contracting with Awareness of Unawareness . . . . . . . . . . . . 42
3.2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.3 Language and Contracts . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.4 Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.5 Framing Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.6 Insurance Contracts . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2.7 Force majeure Clauses . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2.8 Persuasive Advertising . . . . . . . . . . . . . . . . . . . . . . . . 67
vvi CONTENTS
3.2.9 Framing the Future and Self-Control Problems . . . . . . . . . . . 71
3.2.10 Contracts and Interpretation . . . . . . . . . . . . . . . . . . . . 72
3.3 Bayesian Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.3.1 Costly Cognition and Endogenized Describability . . . . . . . . . 81
3.3.2 Asymmetric Awareness and Mis-selling . . . . . . . . . . . . . . . 83
4 Unawareness of Actions 113
4.1 Contractual Traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.1.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.1.2 Solution Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.1.3 A Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . 134
4.1.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.2 Unaware Consumers and Exploitations . . . . . . . . . . . . . . . . . . . 138
4.3 Unaware Agents and Incentive Designs . . . . . . . . . . . . . . . . . . . 140
4.3.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.3.2 The Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.3.3 Heterogeneous Awareness . . . . . . . . . . . . . . . . . . . . . . 150
4.3.4 Justi ability of Contracts . . . . . . . . . . . . . . . . . . . . . . 160
4.3.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 161
5 Conclusion 169
A Appendix 171
A.1 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
A.1.1 Proof of Proposition 3.1 . . . . . . . . . . . . . . . . . . . . . . . 171
A.1.2 Proof of Lemma 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 172
A.1.3 Proof of Proposition 3.3 . . . . . . . . . . . . . . . . . . . . . . . 173
A.1.4 Proof of Lemma 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 173
A.1.5 Proof of Lemma 3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . 173
A.1.6 Proof of Lemma 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . 174
A.1.7 Proof of Proposition 3.4 . . . . . . . . . . . . . . . . . . . . . . . 175
A.1.8 The Insurance Problem under Justi ability Constraint . . . . . . 176CONTENTS vii
A.1.9 Proof of Proposition 3.5 . . . . . . . . . . . . . . . . . . . . . . . 176
A.1.10 Proof of Proposition 3.6 . . . . . . . . . . . . . . . . . . . . . . . 177
A.1.11 Game Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
A.1.12 An In nite-Horizon Bargaining Game where the Buyer makes All
the O ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
A.1.13 Multiple Buyers in the Pooling Equilibrium . . . . . . . . . . . . 179
0A.1.14 A Litigation Process to Punish type-A seller and Reward the Buyer180
A.1.15 Connection to Games with Unawareness . . . . . . . . . . . . . . 181
A.1.16 The Case where Assumption 3.5 fails . . . . . . . . . . . . . . . . 181
A.1.17 Proof of Proposition 3.9 . . . . . . . . . . . . . . . . . . . . . . . 183
A.1.18 Proof of zero-rewarding whenA is appropriate at the post-contractual
stage in Section 3.3.2 . . . . . . . . . . . . . . . . . . . . . . . . . 184
A.1.19 Proof of Proposition 3.15 . . . . . . . . . . . . . . . . . . . . . . . 185
A.1.20 Rationalization of the trap- ltered solution (with cognition) . . . 186
A.1.21 Proof of Proposition 4.2 . . . . . . . . . . . . . . . . . . . . . . . 187
A.1.22 Proof of Proposition 4.3 . . . . . . . . . . . . . . . . . . . . . . . 189Chapter 1
Introduction
Contract theory and economics of information have provided the most successful an-
alytic framework in economic theory in the last thirty years. This paradigm helps us
understand a numerous variety of social problems, say economics, nance, law, man-
agement, politics, and psychology. It raises the explanatory power of economic theory
to a large extent in which classic general equilibrium theory is incompetent. Standard
models in this area include screening, signaling, informed principal theory, mechanism
design, cheap-talk games, information disclosure, information acquisition, information
sharing, information aggregation, moral hazard, collusion, and their extensions to multi-
dimensional or multi-lateral contracting environments, or dynamics. (See, e.g., La ont
and Martimort (2002) and Bolton and Dewatripont (2005).)
Nevertheless, contract theory on its own has limitations. Grossman and Hart (1986)
and Hart and Moore (1990) have introduced an alternative paradigm called incomplete
contracting, which provides an analytic tool to the problem of institutional design. The
basic idea goes as follows. Because some contingencies (or actions) are not veri able, con-
tracting parties have to rely on allocation of control rights to solve the under-investment
problems. However, Maskin (1999), Moore and Repullo (1988) and Maskin and Tirole
(1999) use mechanism design approach to show the irrelevance of veri ability problems
under some conditions. It is suggested that incomplete contracts are as a result of
bounded rationality of contracting parties. However, it is easier said than done. What
we need is a formal and elaborate model of bounded rationality and incomplete contracts.
All standard models in contract theory are based on standard game theory, in which
most solution concepts need the agents’ (high-order) knowledge of rationality and the
game. In standard game theory, an agent i chooses his action s to maximizei
E [u (!;s;s )]!2
i i i
where u is the agent’s utility function, s is the others’ actions, and ! is some payo -i i
relevant contingency for the agents. As a matter of fact, there are many unknown
12 CHAPTER 1. INTRODUCTION
unknowns in our everyday lives. If a person is unaware of something, then he does not
1know it, and he does not know that he does not know it, and so on ad in nitum . Intro-
spection tells us that unawareness is a common kind of ignorance of humans. However,
it is not well-understood in the intellectual world.
In Chapter 2, we discuss the foundation of unawareness. At present, there are two par-
allel ways to approach unawareness: the epistemic approach and the decision theoretic
approach. The epistemic approach starts from agent’s belief. We construct models of
knowledge in the agent’s mind directly. One of the sub-approach initiated by Aumann
(1976) is set-theoretic, or semantic, which is frequently used in economics. The other
approach is syntactic, which is less popular in economics. In contrast, the decision the-
oretic approach starts from the agent’s choice behaviors without referring to the agent’s
belief.
Notably, the thesis focuses on contracting problems with asymmetric awareness between
two contracting parties. Using theoretical models, it studies the behavioral and welfare
implications of unawareness in the market (and within organizations).
First, we discuss unforeseen contingencies and incomplete contracts in Chapter 3. In
terms of games, the agent may not be able to perceive perfectly the entire set of contin-
gencies! in the future. For example, people were unaware that the earth is not at but
actually round long time ago. In the industrial revolution period, people were unaware
of the future global warming. In the economic context, there are many unforeseen events
made by nature. For example, consider that an insuree buys some home insurance. His
probability judgment of the event \calamity" may be smaller than the judgment of the
event \ re, explosion, earthquake, lightning, theft, storm or ood, ", since not all
these states of nature are available in the insuree’s mind when only the general term
\calamity" is mentioned. In this chapter, we model unawareness of contingencies and
its economic implication by non-Bayesian and Bayesian approaches respectively.
Second, we examine unawareness of actions in Chapter 4. The agent is probably not
able to perceive perfectly the other agent’s actions (s ), or his own choice possibilitiesi
(s ). Several years ago, the U.S. people were unaware of September 11, 2001 attacks.i
In the economy, many unforeseen events are directly man-made, that is, an economic
agent’s surprise is the result of the actions of the other agents. For example, a car buyer
may be unaware that the dealer may secretly modify the specs of the car (e.g., whether
the deal includes the air conditioning, built-in GPS, extended warranty, and rear seat
entertainment system) that are not explicitly written in the contract. An insuree may be
unaware that an insurer may delay or withhold the repayments of her life insurance. This
unawareness issue also arises when consumers are surprised by add-on costs of cartridge
1This is the key di erence between unawareness and the other kind of ignorance commonly discussed
in economics, namely uncertainty. If people are uncertain of something, they know that they do not
know it.

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