Resource Allocation in Decentralized Systems with Strategic Agents

113 Pages·2012·0.59 MB·English

Resource Allocation in Decentralized Systems with
Strategic Agents: An Implementation Theory
Approach
by
Ali Kakhbod
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Electrical Engineering: Systems)
in The University of Michigan
2012
Doctoral Committee:
Professor Demosthenis Teneketzis, Chair
Associate Professor Achilleas Anastasopoulos
Professor Mingyan Liu
Assistant Professor Yusufcan Masatlioglu
Associate Professor Asuman Ozdaglar, MIT
(cid:13)c Ali Kakhbod 2012
All Rights Reserved
To my family
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ACKNOWLEDGEMENTS
It is my pleasure to thank the many people who made this thesis possible. I
would like to sincerely thank my advisor Professor Demosthenis Teneketzis for his
continuous support and encouragement, for the opportunity he gave me to conduct
independent research, and for his exemplary respect. I still remember the day when
he had told me, “You will have to believe me about the potential of this field”. Today
when I see the vast scope of research in information economics and its potential to
create an impact on a huge number of applications, I do not have enough words to
thank him for introducing me to this field. His vision, patience, and dedication to
educate his students enabled me to pursue my research in a field that I could have
never imagined before the graduate school. I express my humble gratitude to him for
his friendly and ever inspiring mentorship.
I would also like to thank my dissertation committee members, Professor Achil-
leas Anastasopoulos, Professor Mingyan Liu, Professor Yusufcan Masatlioglu and
Professor Asuman Ozdaglar for accepting to be on my dissertation committee. Their
interest in my research has been a great source of pleasure and motivation for me.
I express my gratitude to Professor Tilman Borgers, Professor Lones Smith and
Professor Daisuke Nakajima for giving me extra time for discussions and providing
me valuable insights on economic concepts.
IfeelgratefultoProfessorAsumanOzdaglarforacceptingtobeonmydissertation
committee despite the fact that she is at MIT.
Thesupportive workand efforts of the staff members ofmy department arehereby
acknowledged. I wish to thank Becky Turanski, Michele Feldkamp, Ann Pace, Karen
Liska and Beth Lawson for efficiently and cheerfully helping me deal with myriad
administrative matters.
I would also like to thank Ashutosh Nayyar and Shrutivandana Sharma for many
discussions and helpful suggestions.
I would like to thank my friends and roommates in Ann Arbor for all their help
and support. Specially, I am thankful to Demos and Barbara for many evenings I
have spent at their home.
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Finally, I am grateful to my family for their endless love and support and for
putting my happiness before their own.
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TABLE OF CONTENTS
DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LIST OF APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
CHAPTER
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Key issues and challenges in resource allocation . . . . . . . . 2
1.3 Contribution of the thesis . . . . . . . . . . . . . . . . . . . . 3
1.4 Organization of the thesis . . . . . . . . . . . . . . . . . . . . 5
II. Implementation Theory . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 What is Implementation Theory? . . . . . . . . . . . . . . . . 6
2.1.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Game Forms/Mechanisms . . . . . . . . . . . . . . 7
2.1.3 Implementation in an appropriate equilibrium concept 9
2.1.4 Implementation in Nash Equilibrium and Maskin’s
Mechanism . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.5 Interpreting Nash Equilibrium . . . . . . . . . . . . 13
2.1.6 Desirable Properties of Game Forms . . . . . . . . . 15
III. Unicast Service Provisioning . . . . . . . . . . . . . . . . . . . . 17
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Contribution of the chapter, (32) . . . . . . . . . . . 17
3.1.2 Comparison with related work . . . . . . . . . . . . 18
3.1.3 Organization of the chapter . . . . . . . . . . . . . . 20
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3.2 The unicast problem with strategic network users,
Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 The centralized problem . . . . . . . . . . . . . . . 20
3.2.2 The decentralized problem with strategic users . . . 22
3.3 A Mechanism for Rate Allocation . . . . . . . . . . . . . . . . 23
3.3.1 Specification of the mechanism . . . . . . . . . . . . 23
3.3.2 Discussion/Interpretation of the Mechanism . . . . 28
3.4 Properties of the Mechanism . . . . . . . . . . . . . . . . . . 30
3.5 Implementation of the decentralized mechanism . . . . . . . . 32
3.6 An Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
IV. Power Allocation and Spectrum Sharing in Multi-user, Multi-
channel Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.1 Contribution of the Chapter, (33) . . . . . . . . . . 35
4.1.2 Comparison with related work . . . . . . . . . . . . 35
4.1.3 Organization of the chapter . . . . . . . . . . . . . . 36
4.2 The Model and Objective . . . . . . . . . . . . . . . . . . . . 37
4.2.1 The Model . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 A Mechanism for Power Allocation and Spectrum Sharing . . 41
4.4 Interpretation of the Mechanism . . . . . . . . . . . . . . . . 42
4.5 Properties of The Mechanism . . . . . . . . . . . . . . . . . . 43
V. Multi-rate Multicast Service Provisioning . . . . . . . . . . . . 51
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.1.1 Motivation and Challenges . . . . . . . . . . . . . . 51
5.1.2 Why is strategic behavior justified? . . . . . . . . . 52
5.1.3 Contribution of the chapter, (34) . . . . . . . . . . . 52
5.1.4 Comparison with related work . . . . . . . . . . . . 53
5.1.5 Organization of the chapter . . . . . . . . . . . . . . 53
5.2 Themulti-ratemulticastproblemwithstrategicnetworkusers,
Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 54
5.2.1 The centralized problem . . . . . . . . . . . . . . . 54
5.2.2 The decentralized problem with strategic users . . . 56
5.2.3 Key features/natures of the problem . . . . . . . . . 58
5.3 A Mechanism for Rate Allocation . . . . . . . . . . . . . . . . 59
5.3.1 Guidelines for the design of the mechanism . . . . . 59
5.3.2 Specification of the mechanism . . . . . . . . . . . . 60
5.3.3 Discussion/Interpretation of the Mechanism . . . . 67
5.4 Properties of the Mechanism . . . . . . . . . . . . . . . . . . 69
VI. Summary and Future Directions . . . . . . . . . . . . . . . . . . 72
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6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.2.1 Algorithmic issues . . . . . . . . . . . . . . . . . . . 73
6.2.2 Dynamic environments . . . . . . . . . . . . . . . . 73
6.2.3 Beyond quasi-linear forms . . . . . . . . . . . . . . 74
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
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LIST OF APPENDICES
Appendix
A. Appendix for Unicast Service Provisioning . . . . . . . . . . . . . . . 76
B. Appendix for Multi-rate Multicast Service Provisioning . . . . . . . . 87
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ABSTRACT
Resource Allocation in Decentralized Systems with Strategic Agents: An
Implementation Theory Approach
by
Ali Kakhbod
Chair: Demosthenis Teneketzis
In this thesis we present an implementation theory approach to decentralized re-
source allocation problems with strategic users/agents in communication networks.
For wired networks we study the unicast and multi-rate multicast service provision-
ing problem. For wireless networks we study the problem of power allocation and
spectrum sharing where each user’s transmissions create interference to all (or subset
of) network users.
We formulate the unicast service provisioning problem as a market allocation
problem, the power allocation and spectrum sharing problem as a public goods al-
location problem, and the multi-rate multicast service provisioning problem as the
combination of a market and a public goods allocation problems.
For unicast and multi-rate multicast service provisioning we develop game
forms/mechanisms that possess the following properties. (P1) The allocations corre-
sponding to all Nash equilibria (NE) of the games induced by the mechanisms are
optimal solutions of the corresponding centralized allocation problems where the ob-
jective is the maximization of the sum of the users’ utilities. (P2) The strategic users
voluntarily participate in the allocation process. (P3) The budget is balanced at the
allocations corresponding to all NE of the game induced by the mechanism as well
as at all other feasible allocations. For the power allocation and spectrum sharing
problem we develop a game form/mechanism that possesses properties (P2) and (P3)
above along with the following property. (P4) The allocations corresponding to all
NE of the game induced by the mechanism are Pareto optimal.
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