Strategic Analysis of Resource Allocation and Public Choice

104 Pages·2013·0.56 MB·English

Strategic Analysis of Resource Allocation and
Public Choice
by
Nanyang Bu
Submitted in Partial Fulfillment of the
Requirements for the Degree
Doctor of Philosophy
Supervised by Professor William Thomson
Department of Economics
Arts, Sciences and Engineering
School of Arts and Sciences
University of Rochester
Rochester, New York
2013
ii
To my parents
Xiaoyang Jiang and Maohua Bu
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Biographical Sketch
TheauthorwasborninHunan, China. HeattendedtheHongKongUniversity
of Science and Technology from 2003 to 2007, and graduated with a Bachelor of
Science degree in Economics and Finance. He attended the graduate program
in economics at the University of Rochester in 2007. He received a Master of
Arts degree from the University of Rochester in 2009. He pursued his research in
Microeconomic Theory under the supervision of Professor William Thomson.
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Acknowledgments
I owe my deepest gratitude to my advisor William Thomson for continuous
and dedicated guidance for my doctoral study. Without him this work would not
have been possible.
I am very much thankful to Paulo Barelli, Srihari Govindan, Asen Kochov,
and Romans Pancs for constant support and helpful advice. I have also bene-
fited greatly from discussions with Azar Abizada, Siwei Chen, Wonki Cho, Battal
Dog˘an, Eun Jeong Heo, Vikram Manjunath, Will Phan, Karol Szwagrzak, Ryan
Tierney, and Ay¸se Yazıcı.
Special thanks to Xiaozhou Li, Fen Qiu, Hui Wang, Bin Yang, and Ruyuan
Zhang for friendship. They paint my life in the brightest colors.
I want to thank Yiran Song, the girl who I love and cherish, for bringing me joy
and peace. I cannot find words to express my gratitude to my parents, Xiaoyang
Jiang and Maohua Bu. Their love is my warmest support.
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Abstract
This thesis consists of a collection of essays on strategic notions on resource allo-
cation and public choice.
In Chapter 1, we study the problem of assigning object types. Each type has
a number of copies. Each individual is assigned at most one object. We examine
some desirable axioms. Our result is that the sequential priority rules are the
only rules that satisfy weak non-wastefulness, weak neutrality, strategy-proofness,
resource monotonicity, and bilateral consistency.
In Chapter 2, we study the problem of assigning objects to buyers with trans-
fers. Each buyer’s preference space contains, but is not limited to, the quasi-linear
preferences. We are concerned about the possibility that a group of buyers may
engage in the following kind of manipulation: they make side payments internally
and then carry out a joint misrepresentation. A rule is strongly group strategy-
proof ifnogroupcangainbyengaginginsuchoperations. Wealsoconsiderseveral
other appealing requirements. We find that the posted-price rules are the only
rules that satisfy non-triviality, non-imposition, envy-freeness, and strong group
strategy-proofness.
In Chapter 3, we study the general problem of public choice. We consider
environments where agents’ identities may not be observable. An agent may
create fictitious identities and submit multiple preference relations under them.
We study false-name-proofness, the requirement that no agent should ever gain
via such operations. Our main result is that if a rule is anonymous, strategy-proof,
and population monotonic, then it is false-name-proof; if the preference domain
contains only strict preference relations, the converse also holds.
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In Chapter 4, we study the school choice problem. All previous literature
assumes that applications to schools are costless. In reality, however, making
a school as a choice is always costly. We aim to compare all prominent rules.
We study the induced ranking revelation games associated with them. We find
that no matter how small the costs are, these rules are strategically equivalent;
moreover, for each of them and each preference profile, the set of Nash equilibrium
matchings of the induced ranking revelation game associated with it is the set of
stable matchings for the true preferences.
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Contributors and Funding
Sources
This work was supervised by a dissertation committee consisting of Professors
WilliamThomson(advisor)andProfessorPauloBarellioftheDepartmentofEco-
nomics and Professor Tasos Kalandrakis of the Department of Political Science.
All work for the dissertation was completed independently by the student.
Table of Contents
Chapter 1 Characterizations of the Sequential Priority Rules in
the Assignment of Object Types 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Definitions and notations . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Chapter 2 Joint Misrepresentation with Bribes 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Definitions and notations . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Main result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Independence of the axioms . . . . . . . . . . . . . . . . . . . . . 37
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Chapter 3 Unfolding the Mystery of False-name-proofness 41
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
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Chapter 4 Costly School Choice 51
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Definitions and notations . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 The axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4 The rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.5 The induced ranking revelation game . . . . . . . . . . . . . . . . 72
4.6 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.7 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Bibliography 91
Chapter 1
Characterizations of the
Sequential Priority Rules in the
Assignment of Object Types
1.1 Introduction
A university housing office has to assign housing to graduate students. There are
different types of units: some are studios and others are rooms in two-bedroom
apartments; some are furnished and others not. There may be multiple units
of each type. When filling out their applications, students rank the different
types. How should the rooms be assigned? This is the kind of situations that we
consider. Moregenerally, westudytheproblemofassigningasocialendowmentof
indivisible resources, called “object types”, or “objects” for short, to a population
of individuals. Monetary compensation is not allowed. We refer to the number
1