OR models and algorythms to solve multi-actor heterogeneous decision problems

160 Pages·2007·3.62 MB·English

by  M. Elena Sáiz

Game Theory at Work:
OR models and algorithms to solve multi-actor
heterogeneous decision problems

Game Theory at Work:
OR models and algorithms to solve multi-actor
heterogeneous decision problems
M. Elena Sa´iz
Proefschrift
ter verkrijging van de graad van doctor
op gezag van de rector magnificus
van Wageningen Universiteit,
Prof. dr. M.J. Kropff,
in het openbaar te verdedigen
op woensdag 24 oktober 2007
des namiddags te half twee in de Aula
GameTheoryatWork: ORmodelsandalgorithmstosolvemulti-actorheterogeneous
decision problems
PhD thesis Wageningen Universiteit - with references - with summaries in English,
Dutch and Spanish
Sa´iz M. E., 2007
ISBN: 978-90-8504-769-8
Promotor: Prof. ir. A.J.M. Beulens
HoogleraarToegepaste Informatiekunde
Prof. dr. ir. J.G.A.J. van der Vorst
HoogleraarLogistiek en Operationele Research
Co-promotor: Dr. E.M.T. Hendrix
Universitair Hoofddocent bij de Leerstoelgroep
Operationele Research en Logistiek
Samenstelling promotiecommissie:
Prof. dr. F. Plastria Vrije Universiteit Brussel
Prof. dr. J. Puerto Albandoz Universidad de Sevilla
Prof. dr. A.M.A. van Deemen Radboud Universiteit Nijmegen
Prof. dr. E.C. van Ierland Wageningen Universiteit
Dit onderzoek is uitgevoerd binnen de Mansholt Graduate School of Social Sciences.

Abstract
The objective of this thesis is to explore the potential of combining Game Theory (GT)
modelswithOperationsResearch(OR)modelling. Thisincludesdevelopmentofalgorithms
to solvethese complex OR models for different empirical situations. The challenge is to get
GT“atwork”byapplyingsuchmodelsandtechniquestopracticalcases. Fourdifferentcases
with a challenge on thedevelopment of algorithms are studied.
A first case illustrates a multiple coalition formation game in which membership rules and
different transfer schemes are described. Given the GT model and the OR model, the goal
is to develop methods for checking stability of coalition structures. A new mathemati-
cal programming formulation, crucial for the development of the algorithms, is elaborated.
Available data is used to determine which stable coalitions appear and which procedures
(transfer schemes) can be used to make coalitions stable. Also the influenceof membership
rules(whetheractorsarefree tobecomeamember)isinvestigated. Main conclusion isthat
transferschemesareusefultobeimplementedtoobtainstablecoalitions. Moreover,different
membershiprules,e.g. vetoormajorityvotingofcurrentmembers,generatedifferentresults
with and without transfer schemes.
Asecondcasestudiesamodelofcoalitionformationinpoliticswithnpartiestryingtoform
a government. Given the number of parties n and policy dimension m (number of items),
computationalalgorithmsaredevelopedtocomputeallpossiblemajoritycoalitionsandpref-
erencesofpartiesoverthosecoalitions. ApplicationtoDutchdataandtheoreticalexamples
leadstotestingofhypotheseswithsurprisingresultswithrespecttocoalitionformationsuch
as: being a first mover is not necessarily advantageous, being less flexible is not necessarily
advantageous, forming a minimal winning coalition is not necessarily advantageous.
A third case describes a two-stage location-quantitygame where n>2 firms are competing
onm>2markets. Thespacewherethefirmscanlocatearenodesonanetwork. Analytical
solutionsforthesupplyingdecisionsandpropertiesfordeterminingthenumberofsuppliers
toeachmarketarederived. Infindingtheequilibria,acompleteenumerationalgorithmand
alocal searchalgorithm areused. Twocasesareelaborated toillustratetheproceduresand
theanalytical results.
The last case deals with a competitive facility location problem in which the concept of
Stackelbergleader-followerproblemisapplied. Thefollowerproblemandleaderproblemare
global optimisation problems. Branch-and-Bound (B&B) algorithms that guarantee to find
theoptimum of both problems are designed.
Key words: Game theory,operations research, optimisation methods,algorithms.

Preface
By doing a PhD abroad, one is confronted with the cultureetiquettes. As Spaniard,I tried
to explain that we havesun but also snow; that we donot always takea“siesta”but along
lunch-breakand keepworking until6,7 or8 p.m., wehavecentralheatingand we havethe
beautiful letter“n˜”, without“her”what would happen with“man˜ana”...? We do not make
appointmentswithfriends,wejustsimplycallandmeetlaterthesamedayor“man˜ana”,we
donothavesomanyrulesleadingto“if-then”behaviour,wedonothaveabirthdaycalendar
in the toilet, we just remember or forget the birthdays, but it is well accepted by friends.
Yes, we are very good with jokes but we do not always speak so loud ...only when we are
more than two.
EverythingstartedinSevilla. Atthebeginningofthesummerof2001ImovedtoSevilla
to start my PhD studies at the department of Statistics and Operations Research. There,
the Professor of the group assigned Rafael Blanquero as my supervisor. Thanks to Rafa
I became enthousiastic about the PhD, and thanks to Rafa I came to Wageningen. Rafa,
without you today would not havebeen possible.
I would like to thank my promoters Prof. ir. Adrie J.M. Beulens, Prof. dr. ir. Jack
G.A.J. van der Vorst and my daily supervisor and co-promotor Dr. Eligius M.T. Hendrix.
Adrie and Jack, first of all thanks for all the support, assistance, encouragement, criticism
and philosophical questions during our meetings. I have learnt a lot from them, as you
surely know. Adrie, thanks for all your active, positive, productive comments, and for
always having a smile for everything. Jack, what can I say, since you arrived to our group
everything changed ...to be better. Already in our first meeting I was impressed. At that
moment I was already in my second year of PhD without any research question and any
proposal,justgoingonhereandthere. Youaretheresponsibleongettingfundsforthefinal
two years of this adventure. You taught me lot of things during the meetings. For both,
thanksforallthethinkingonwhatisthisthesisabout,whataretheresearch questionsand
foralltheinputonmy“researcher”education. Eligius,thankyouforyourpatient,guidance,
thanks for all the thinkings, ideas, support, encouragement, jokes, we spent many many
hours discussing the research. If I have to evaluate you as a supervisor, for me you are the
best. I will be back toyou later, as family.
IwouldlikenowtothanktothewholeteamofOperationeleResearchenLogistiek: Frits,
thanks for asking now and then how I am doing; Theo, now Real Madrid is doing better
withtheDutchplayersehh;JokeandKarin,thegirls,itwasalwaysfunnytohavesomegirls
gossiping; Niels, we know how to respect and share the bad and good PhD mood, I hope
youwill havea successfulcareer; thenewcomerJelena orEnna,sheintroducedanicedrink
tradition on Fridays. And finally Ria, you were always so positive, kind, and a smile in the
morning, thankyou,I knowthat thebottles of wine were not thereason :-)
And during the last years I would also like to thank the team of Toegepaste Infor-
matekunde: Kees,Rob,GertJan,Ayalew,Dik,Mark,Yuan,Sebastiaan,Gerard,Jan,Kees,
Sjoukje, Huub,Maarten and again ...Ria. I also want to expressmy gratitudeto Paul van
Beek for his helpfulcomments and interest in my research.
People from the Leeuwenborch: Ekko was responsible to bring me here to Wageningen.
ThenI metthewholeSTACOteam. Thankstoall ofyou,youwerealways verysupportive
andnewideaswereonthetableatallofthemeetings. ThankstoJuanCarlos, theMexican
part of theteam. Thanks toRob, Hans-Peterand Michael, clever and wise people.
IwouldliketoexpressmygratitudetoAgnieszkaandAnnelies,Ireally enjoyedtowork
together with you, it was a pleasure. I wish you all the best in your new positions. And
many thanks for introducing me to Ad. I want to express my gratitude to Jos´e Fern´andez
and Blas Pelegr´ın; research via e-mail is difficult but not impossible. Thanks for all the
input-outputof ourcommon research.
Thanksare also extendedto colleagues from theSocial SciencesDepartment: to Amber
and Janneke, I have always enjoyed a lot our coffee breaks outside; to Lan Ge, for sharing
pre-conference nervios and post-talk fun, and for the years in here; to Morteza, my squash
partnerthefirst years. I would like tothank all people from EnvironmentalEconomics and
Natural Resources Group and the Mansholt team. I should also mention the secretaries of
theLeeuwenborch.
Specific gratitude goes to De Bongerd. I have all of the members in my heart. Thanks
alot for helpingmetoget rid of thestress orwhateverI hadin myhead: Rob(2Rob“os”),
Henry, Ren´e, Wendy, John ...but special words go to Ellen and Ingi. Ellen, thanks for
all the very nice moments/talks doing step, indoor biking or whatever out of sports. Sorry
for missing a lot during my last PhD year ...Ingi, thanks for being the one to start an
ongelofelijk-party-team with Ellen, you and me, thanks for the laughs together, the chats,
thekinderen,thegezelligemomentjesandthanksforbeingalwaysthereandforyoursupport,
enthusiasm and ideas about all the weird things I was doing. I must say thank to you for
youbeingas youare. Toboth andall theteam oftheBonderd,thanksfor makingmanyof
my stuff easier.
I must also say thanks to Joanna. Last years were very gezellig, I had a lot of fun and
I would never forget your 2006 birthday party. I would like to express my gratitude to the
RuralcorneroftheLeeuwenborch. JanDouwe,siemprehasconseguidosacarmeunasonrisa,
gracias(todav´ıamedebesunacerveza). SpecialthanksgoestoKeiandGustavoforsharing
PhD up and downs, gracias por todo vuestro apoyo. A big word of thanks goes to Petra. I
had a great time with you talking in Spanutch (siempre curiosa sobre el significado/ra´ız de
muchas palabras), biking and discussing life issues. Ans and Cees, many thanks for taking
care of the PhD team. I will never forget you and your gezellig parties. Ans, thanksgiving
us advice on the layout of our books. I would like to thank all the good friends I have met
during my years in Wageningen, specially to Adolf, Olga, Toni, Marga, (Francesca)2, Axel,
Andre,Aday la u´ltimaen llegar, Noa“RiberadelDuero”. I also wish to thanktoNelly for
keepingmy neck connectingmy head and back.
I would like to thank Costanza, when she was living in Wageningen everything was
different. I am glad that we met and we had/have many talks and discussions about life,
thanksfor sharing that with me. “Jenny”Co,“IlSasha piu` adattato, zio felice, trannenella
pioggia. Un grande bacio e noi manchiamo a voi”:-O . Lola, Paul and Joek (het hondje),
what can I say ...I do not have enough pages to say how important you are in my life,
not only in Wageningen. Thanks for all your support and for the many many many good
momentswehavehad. Thanksforsharingyourfriendship,forcheeringmeupwhenIneeded.
Itmaybehelpedthejamo´n andchorizofor Paultje:-). Outof jokes,I loveyouand youwill
bealways onmy heart andmylife. Specialthanksgoes toLola. I hadgreat timewith you,
thank you for your humor, your encourage, for sharing the good and the bad on our PhD