Fundamentals of evolutionary game theory and its applications /Fundamentals of evolutionary game theory and its applications

223 Pages·2015·8.55 MB·English

Evolutionary Economics and Social Complexity Science 6
Jun Tanimoto
Fundamentals
of Evolutionary
Game Theory
and its
Applications
Evolutionary Economics and Social Complexity
Science
Volume 6
Editors-in-Chief
TakahiroFujimoto,Tokyo,Japan
YujiAruka,Tokyo,Japan
EditorialBoard
SatoshiSechiyama,Kyoto,Japan
YoshinoriShiozawa,Osaka,Japan
KiichiroYagi,Neyagawa,Japan
KazuoYoshida,Kyoto,Japan
HideakiAoyama,Kyoto,Japan
HiroshiDeguchi,Yokohama,Japan
MakotoNishibe,Sapporo,Japan
TakashiHashimoto,Nomi,Japan
MasaakiYoshida,Kawasaki,Japan
TamotsuOnozaki,Tokyo,Japan
Shu-HengChen,Taipei,Taiwan
DirkHelbing,Zurich,Switzerland
The Japanese Association for Evolutionary Economics (JAFEE) always has
adhered to its original aim of taking an explicit “integrated” approach. This path
hasbeenfollowedsteadfastlysincetheAssociation’sestablishmentin1997and,as
well,sincetheinaugurationofourinternationaljournalin2004.Wehavedeployed
anagendaencompassingacontemporaryarrayofsubjectsincludingbutnotlimited
to: foundations of institutional and evolutionary economics, criticism of main-
stream views in the social sciences, knowledge and learning in socio-economic
life, development and innovation of technologies, transformation of industrial
organizations and economic systems, experimental studies in economics, agent-
basedmodelingofsocio-economicsystems,evolutionofthegovernancestructure
offirmsandotherorganizations,comparisonofdynamicallychanginginstitutions
oftheworld,andpolicyproposalsinthetransformationalprocessofeconomiclife.
In short, our starting point is an “integrative science” of evolutionary and institu-
tionalviews.Furthermore,wealwaysendeavortostayabreastofnewlyestablished
methodssuchasagent-basedmodeling,socio/econo-physics,andnetworkanalysis
aspartofourintegrativelinks.
Morefundamentally,“evolution”insocialscienceisinterpretedasanessentialkey
word, i.e., an integrative and/or communicative link to understand and re-domain
variousprecedingdichotomiesinthesciences:ontologicalorepistemological,sub-
jective or objective, homogeneous or heterogeneous, natural or artificial, selfish or
altruistic,individualisticorcollective,rationalorirrational,axiomaticorpsycholog-
ical-based, causal nexus or cyclic networked, optimal or adaptive, microor macro-
scopic, deterministic or stochastic, historical or theoretical, mathematical or
computational,experimentalorempirical,agent-basedorsocio/econo-physical,insti-
tutional or evolutionary, regional or global, and so on. The conventional meanings
adhering to various traditional dichotomies may be more or less obsolete, to be
replaced with more current ones vis-a`-vis contemporary academic trends. Thus we
arestronglyencouragedtointegratesomeoftheconventionaldichotomies.
These attempts are not limited to the field of economic sciences, including
management sciences, but also include social science in general. In that way,
understanding the social profiles of complex science may then be within our
reach. In the meantime, contemporary society appears to be evolving into a
newlyemergingphase,chieflycharacterizedbyaninformationandcommunication
technology (ICT) mode of production and a service network system replacing the
earlier established factory system with a new one that is suited to actual observa-
tions.Inthefaceofthesechangesweareurgentlycompelledtoexploreasetofnew
propertiesforanewsocio/economicsystembyimplementingnewideas.We thus
are keen to look for “integrated principles” common to the above-mentioned
dichotomiesthroughoutourserialcompilationofpublications.Wearealsoencour-
agedtocreateanew,broaderspectrumforestablishingaspecificmethodpositively
integratedinourownoriginalway.
More information about this series at http://www.springer.com/series/11930
Jun Tanimoto
Fundamentals of
Evolutionary Game Theory
and its Applications
JunTanimoto
GraduateSchoolofEngineeringSciences
KyushuUniversityInterdisciplinary
Fukuoka,Fukuoka
Japan
ISSN2198-4204 ISSN2198-4212 (electronic)
EvolutionaryEconomicsandSocialComplexityScience
ISBN978-4-431-54961-1 ISBN978-4-431-54962-8 (eBook)
DOI10.1007/978-4-431-54962-8
LibraryofCongressControlNumber:2015951623
SpringerTokyoHeidelbergNewYorkDordrechtLondon
©SpringerJapan2015
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Preface
For more than 25 years, I have been studying environmental issues that affect
humans,humansocieties,andthelivingenvironment.Istartedmyresearchcareer
by studying building physics; in particular, I was concerned with hygrothermal
transferproblemsinbuildingenvelopesandpredictionsofthermalloads.Aftermy
Ph.D. work, I extended my research field to a special scale perspective. This
extension was motivated by several factors. One was that I noticed a reciprocal
influence between an individual building environment and the entire urban envi-
ronment.Another wasthat theso-called urban heatisland problem began todraw
much attention in the 1990s. Mitigation of urban heating contributes to energy
conservation and helps improve urban amenity; hence, the urban heat island
problembecameoneofthemostprominentsocialissuesofthetime.Thus,Istarted
tostudyurbanclimatologybecauseIwasmainlyconcernedwithwhyandhowan
urban heat island forms. The problem was approached with sophisticated tools,
such as wind tunnel experiments, field observations, and computational fluid
dynamics (CFD), and was backed by deep theories concerning heat transfer and
fluid dynamics. A series of such studies forced me to realize that to obtain
meaningful and reasonable solutions, we should focus not only on one area (e.g.,
the scale of building physics) but also on several neighboring areas that involve
complexfeedback interactions(e.g., scales ofurban canopiesandofurban clima-
tology).Itiscruciallyimportanttoestablishnewbridgesthatconnectseveralareas
havingdifferentspatiotemporalscales.
Thisexperiencemademerealizeanothercrucialpoint.Theterm“environment”
encompasses a very wide range of objects: nature, man-made physical systems,
society, and humanity itself. One obvious fact is that we cannot achieve any
significant progress in solving so-called environmental problems as long as we
focusonjustasingleissue;everythingisprofoundlyinterdependent.Turningonan
airconditionerisnotthefinalsolutionforfeelingcomfortable.Theoperationofan
air conditioner increases urban air temperatures; therefore, the efficiency of the
overall system inevitably goes down and more energy must be provided to the
system. This realization might deter someone from using an air conditioner. This
v
vi Preface
situationisoneintelligibleexample.Thedecisionsofanyindividualhumanaffect
the environment,and the decisions ofasocietyasa collectionofindividuals may
substantially impact the environment. In turn, the environment reacts to those
decisions made by individuals and society, and some of that feedback is likely to
be negative. Such feedback crucially influences our decision-making processes.
Interconnectedcyclingsystemsalwaysworkinthisway.
With this realization, I recognized the concept of a combined human–
environmental–social system. To reach the crux of the environmental problem,
which includes physical mechanisms, individual humans, and society, we must
studythecombinationofthesediversephenomenaasanintegratedenvironmental
system. We must consider all interactions between these different systems at all
scales.
I know well that this is easy to say and not so easy to do. I recognize the
difficulties in attempting to establish a new bridge that connects several fields
governedbycompletelydifferentprinciples,suchasnaturalenvironmentalsystems
andhumansystems.IunderstandthatIstandbeforeasteepmountainpath.
Yet, I have seen a subtle light in recent applied mathematics and physics that
includes operations research, artificial intelligence, and complex science. These
approaches help us model human actions as complex systems. Among those,
evolutionary game theory seems to be one of the most powerful tools because it
gives us a clear-cut template of how we should mathematically treat human
decision making, and a thorough understanding of decision making is essential to
build that new bridge. Thus,for the last decade, Ihave been deeply committed to
thestudyofevolutionarygametheoryandstatisticalphysics.
This book shares the knowledge I have gained so far in collaboration with
graduate students and other researchers who are interested in evolutionary game
theoryanditsapplications.Itwillbeagreatpleasureformeifthisbookcangive
readers some insight into recent progress and some hints as to how we should
proceed.
InterdisciplinaryGraduateSchoolofEngineering JunTanimoto
Sciences,KyushuUniversity
Fukuoka,Japan
Acknowledgments
This book owes its greatest debt to my coworkers who had been my excellent
students.Chapter2reliesatcriticalpointsonthecontributionsofDr.HirokiSagara
(Panasonic Factory Solutions Co. Ltd.) and Mr. Satoshi Kokubo (Mitsubishi
ElectricCorporation).Dr.AtsuoYamauchi(MeidenshaCorporation),Mr.Satoshi
Kokubo, Mr. Keizo Shigaki (Rico Co. Ltd.), Mr. Takashi Ogasawara (Mitsubishi
Electric Corporation), and Ms. Eriko Fukuda (Ph.D. candidate at Kyushu Univer-
sity)gaveverysubstantialinputtothecontentofChap.3.Chapter5wouldnothave
been completed without the many new findings of Dr. Atsuo Yamauchi,
Mr. Makoto Nakata (SCSK Corporation), Mr. Shinji Kukida (Toshiba Corpora-
tion),Mr.KezoShigaki,andMr.TakuyaFujiki(ToyotaMotorCorporation)based
on the new concept that traffic flow analysis can be dovetailed with evolutionary
game theory. Chapter6isthe productofdedicated effortbyMs.ErikoFukuda in
seekinganotherinterestingchallengethatcanbeaddressedwithevolutionarygame
theory. I sincerely express my gratitude to these people as well as to Dr. Zheng
Wang (JSPS [Japan Society for the Promotion of Science] Fellow at Kyushu
University) who works with our group, is regarded as one of the keenest young
scholars,anddealswithgameandcomplexnetworktheory.Continuousdiscussions
with allthese collaborators have helpedmeadvanceourstudies andrealizemuch
satisfactionfromourefforts.
IamalsogratefultoDr.Prof.YujiArukaatChuoUniversityforgivingmethe
opportunitytopublishthisbook.
vii
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Contents
1 Human–Environment–SocialSystemandEvolutionary
GameTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ModelingaRealComplexWorld. . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 EvolutionaryGameTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 StructureofThisBook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 FundamentalTheoryforEvolutionaryGames. . . . . . . . . . . . . . . . . 7
2.1 LinearDynamicalSystems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Non-linearDynamicalSystems. . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 2-Player&2-Stratey(2(cid:1)2)Games. . . . . . . . . . . . . . . . . . . . . . 14
2.4 DynamicsAnalysisofthe2(cid:1)2Game. . . . . . . . . . . . . . . . . . . . . 22
2.5 Multi-playerGames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.6 SocialViscosity;ReciprocityMechanisms. . . . . . . . . . . . . . . . . . 30
2.7 UniversalScalingforDilemmaStrengthin2(cid:1)2Games. . . . . . . 32
2.7.1 ConceptoftheUniversalScalingforDilemmaStrength. . . 34
2.7.2 AnalyticalApproach. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7.3 SimulationApproach. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.8 R-ReciprocityandST-Reciprocity. . . . . . . . . . . . . . . . . . . . . . . . 56
2.8.1 ST-ReciprocityinPhase(I). . . . . . . . . . . . . . . . . . . . . . . 63
2.8.2 ST-ReciprocityinPhase(II). . . . . . . . . . . . . . . . . . . . . . . 63
2.8.3 ST-ReciprocityinPhase(III). . . . . . . . . . . . . . . . . . . . . . 64
2.8.4 ST-ReciprocityinPhase(IV). . . . . . . . . . . . . . . . . . . . . . 65
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3 NetworkReciprocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.1 WhatIsMostInfluentialtoEnhanceNetworkReciprocity?Is
TopologySoCriticallyInfluentialonNetworkReciprocity?. . . . . 70
3.1.1 ModelDescription. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.1.2 ResultsandDiscussion. . . . . . . . . . . . . . . . . . . . . . . . . . 75
ix