Table Of ContentSPRINGER BRIEFS IN ELECTRICAL AND COMPUTER
ENGINEERING CONTROL, AUTOMATION AND ROBOTICS
Juntao Chen
Quanyan Zhu
A Game- and
Decision-Theoretic
Approach to Resilient
Interdependent
Network Analysis and
Design
123
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Juntao Chen Quanyan Zhu
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A Game- and Decision-
Theoretic Approach
to Resilient Interdependent
Network Analysis
and Design
123
Juntao Chen QuanyanZhu
Department ofElectrical andComputer Department ofElectrical andComputer
Engineering,TandonSchoolofEngineering Engineering,TandonSchoolofEngineering
NewYork University NewYork University
Brooklyn, NY,USA Brooklyn, NY,USA
ISSN 2191-8112 ISSN 2191-8120 (electronic)
SpringerBriefs inElectrical andComputer Engineering
ISSN 2192-6786 ISSN 2192-6794 (electronic)
SpringerBriefs inControl, Automation andRobotics
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To our families
Juntao Chen and Quanyan Zhu
Preface
Thisbookprovidesanoverviewofgameanddecisiontheoreticmethodsfordesigning
resilient and interdependent networks. The book aims to unite game theory with
networksciencetolayasystem-theoreticfoundationforunderstandingtheresiliency
ofinterdependentandheterogeneousnetworksystems.Onefocusedapplicationarea
of the book is the critical infrastructure systems. Infrastructure networks such as
electric power, water, transportation, and communications are increasingly inter-
connectedwiththeintegrationofInternetofThingsdevices.Asingle-pointshutdown
ofageneratorintheelectricpowereitherduetocyberandphysicalattacksornatural
failures can propagate to other infrastructures and creates an enormous social and
economic impact. Therefore, secure and resilient design of interdependent critical
infrastructureiscritical.Toachievethisgoal,itrequiresmultidisciplinaryresearchin
thisareathatcrosscutscomputerscience,engineering,publicpolicy,socialsciences,
and mathematics. The book summarizes recent research findings into three parts
including resilient meta-network modeling and analysis, control of interdependent
epidemicsspreadingoverlarge-scalecomplexnetworks,andapplicationstocritical
infrastructuressuchasInternetofbattlefieldthings.Eachchapterincludesasectionon
background, which does not require the readers of this book to have advanced
knowledgeingameanddecisiontheoryandnetworkscience.
The book is self-contained and can be adopted as a textbook or supplementary
reference book for courses on network science, systems and control theory, and
infrastructures. The book will be also useful for practitioners or industrial
researchers across multiple disciplines including engineering, public policy, and
computersciencewholookfornewapproachestoassessandmitigaterisksintheir
systems and enhance their network resilience.
The authors would like to thank fruitful discussions and collaborations with
CorrineTouati(INRIA,France),RuiZhang(NYU),andotherresearchmembersin
NYU Tandon LARX. The authors would also like to acknowledge support from
NSF and DHS.
Brooklyn, NY, USA Juntao Chen
May 2019 Quanyan Zhu
vii
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation and Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Overview of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Background of Game Theory and Network Science . . . . . . . . . . . . . 5
2.1 Introduction to Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Finite Nash Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Infinite Nash Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Stackelberg Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Basics of Network Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Modeling of Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Modeling of Network-of-Networks . . . . . . . . . . . . . . . . . . 9
2.3 Notation Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Meta-Network Modeling and Resilience Analysis . . . . . . . . . . . . . . . 13
3.1 Static Network Resilience Game . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.2 Nash Equilibrium Analysis. . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.3 Algorithm Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.4 SDP-Based Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.5 Alternative Problem Formulation . . . . . . . . . . . . . . . . . . . 20
3.1.6 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Dynamic Network Resilience Game. . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Games-in-Games Framework . . . . . . . . . . . . . . . . . . . . . . 27
3.2.2 Problem Analysis and Meta-Equilibrium. . . . . . . . . . . . . . 32
3.2.3 SDP-Based Approach and Online Algorithm. . . . . . . . . . . 36
3.2.4 Adversarial Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.5 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
ix
x Contents
3.3 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Interdependent Decision-Making on Complex Networks. . . . . . . . . . 49
4.1 Interdependent Epidemics on Large-Scale Networks. . . . . . . . . . . 49
4.2 Controlling Interdependent Epidemics on Complex Networks . . . . 50
4.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.2 Network Equilibrium and Stability Analysis . . . . . . . . . . . 54
4.2.3 Optimal Quarantining Strategy Design . . . . . . . . . . . . . . . 59
4.2.4 Equilibria Switching via Optimal Quarantine. . . . . . . . . . . 65
4.2.5 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5 Optimal Secure Interdependent Infrastructure Network Design. . . . 75
5.1 Interdependent Infrastructure Network Security . . . . . . . . . . . . . . 75
5.2 OptimalSecureTwo-LayerNetworkDesignwithanApplication
to IoBT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.1 Heterogeneous Two-Layer IoT Network Design
Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2.2 Analytical Results and Optimal IoT Network Design. . . . . 81
5.2.3 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Future Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Chapter 1
Introduction
1.1 Motivation andIntroduction
OurworldisincreasinglyconnectedduetotheadoptionofsmartdevicesandInternet
ofThings(IoT).Notonlydoestheconnectivityofthenetworkitselfgrowsbutalso
networks areinterconnected withother networks which create interdependent net-
works. For example, the power networks are nowadays integrated with communi-
cation networks with the advances of the smart grid technologies. Transportation
networksareconnectedwithsocialnetworksthroughon-demandtransportsystems.
Thedeeplyinterconnectedcyber-physical-socialnetworkscreatenewchallengesfor
improvingtheresiliencyatdifferentscalesagainstallhazardsfromnature,terrorism,
anddeliberatecyberattacks.
The first challenge of designing resilient interdependent networks comes from
thelackofsystemframeworkthatcapturesheterogeneousnetworkcomponents.The
existingmodelsinliteraturearemostlydesignedforasingle-layernetworkcontaining
a number of agents. In this book, we propose a network-of-networks framework
that jointly considers the interactions within a network itself and across different
layers of networks. This framework facilitates the analysis of network operators’
strategies whose objectives and actions are coupled due to the inherent network
interdependencies.Thenetwork-of-networksmodelingoffersaholisticviewofthe
separate components by leveraging which we can analyze the system-of-systems
performanceoftheglobalnetwork.
Thesecondchallengefordesigningresilientinterdependentnetworkistheunco-
ordinatednaturebetweensystemdesigners.Thischaracteristichasbeenobservedina
numberofscenarios.Forexample,thepowersystemandtransportationsystemopera-
torsdeterminetheiroperationalpoliciesseparatelywithagoalinimprovingtheirown
revenueeventhoughthesetwonetworksarecoupled.Thisdecision-makingpatternis
differentfromsingle-layernetworkwherethedesignermaximizestheglobalsystem
utility.Toaddressthisdistinctchallengeininterdependentnetworks,weestablisha
game-theoretic frameworktocapturethedecentralizednatureofdecision-making.
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J.ChenandQ.Zhu,AGame-andDecision-TheoreticApproachtoResilient
InterdependentNetworkAnalysisandDesign,SpringerBriefsinControl,
AutomationandRobotics,https://doi.org/10.1007/978-3-030-23444-7_1
