Manuel Alfredo Mosquera Rodríguez's PhD Thesis - Departamento

130 Pages·2007·0.96 MB·English

UNIVERSIDADE DE SANTIAGO DE COMPOSTELA
Departamento de Estatística e Investigación Operativa
ESSAYS ON OPERATIONS RESEARCH GAMES AND
CAUTIOUS BEHAVIOR
ManuelAlfredoMosqueraRodríguez
SantiagodeCompostela,February2007
Supported by the Ministerio de Educación y Ciencia, FEDER and Xunta de Galicia under projects BES-2003-1277,
BEC2002-04102-C02-02,SEJ2005-07637-C02-2andPGIDIT03PXIC20701PN.
Realizadoelactopúblicodedefensaymantenimientodeestatesisdoctoraleldía2defebrero
de 2007, en la Facultad de Matemáticas de la Universidad de Santiago de Compostela, ante el
tribunalformadopor:
Presidente: Dr.D.JoséManuelZarzueloZarzosa
Vocales: Dr.D.PeterBorm
Dr.D.MarkVoorneveld
Dr.aD.aEstelaSánchezRodríguez
Secretaria: Dr.aD.aBalbinaVirginiaCasasMéndez
siendodirectoreslaDr.aD.aMaríaGloriaFiestrasJaneiroyelDr.D.IgnacioGarcíaJurado,obtu-
volamáximacalificacióndeSOBRESALIENTECUMLAUDE.Además,estatesishacumplido
losrequisitosnecesariosparalaobtencióndelDOCTORADOEUROPEO.

AYoli,mispadresymihermano.
Gracias.

Preface
Someyearsago,IhadtodecidewhichbachelorIshouldtake. TheBachelorofMathematicswas
notmyfirstoption,butbecauseofseveralreasonsIhadtochooseit. Thefirstyearwasnotfully
pleasant because I had in mind to change my studies. However, during that year, I started to
discover the world of Mathematics and decided to continue once year more. Year after year, I
wasmoreandmoreinterestedbythewonderfuluniverseofMathematics.
InmyfifthBachelor’syear,IfollowedacourseingametheorybyIgnacioGarcíaJurado. It
wastherewheremyinterestinthefieldofgametheorywasborn. ThenextyearIbecameaPhD
student in the Department of Statistics and Operations Research of the University of Santiago
de Compostela. Ignacio García Jurado and Gloria Fiestras Janeiro became my advisors. They
helped me a lot during my years as a PhD student, not only in the academic field, but also in
makingdecisionsaboutmyfuture. IamindebtedtothemforacceptingmeastheirPhDstudent
andforbeingpatientwithmystubbornness. ThanksIgnacioandGloria!
Also Ignacio and Gloria have been my link with prestigious researchers in game theory. I
hadthegoodluckofworkingwithsomeofthemandIhavelearnedofthemhowtomakegood
research. Iamindebtedtoallofmyco-authors,Arantza,Gloria,Herbert,Ignacio,JoséManuel,
Mark,andPeter. Also,Iwanttothanktomy(ex-)officemateJulioforthefruitfulcommentsand
discussionsonsometopicsthanwehavehad.
Through my years as a PhD student I could visit a lot of prestigious research centers like
TilburgUniversity,BasqueCountryUniversity,StockholmSchoolofEconomicsandUniversitat
AutònomadeBarcelona. There,IknewalotofpeopleandIcouldexperimentdifferentwaysof
researching;thesetwoaspectshavehelpedmetohaveawideperspectiveongametheoryand
related fields. I want to thank to Peter for hosting me in the Department of Econometrics and
Operations Research of University of Tilburg (once was not enough, I was there three times),
andtoArantza, Herbert, Mark, Henk, Ruud, Baris, Emiliya, Corrado, ...andothersatCentER
forthegreatatmospherethatIfoundthere. AnspecialmentionisdeservedtoArantza. Shewas
mySpanishlinkwiththepeopleinTilburg;withoutherhelpmyvisitshadnotbeensofruitful.
IamindebtedtoMarkforhostingmeatStockholmSchoolofEconomicsandforworkingwith
mealsoduringmyvisitstoTilburgUniversity. IamgratefultoJoséManuelforhavinginvited
metotheDepartmentofAppliedEconomicsIVoftheBasqueCountryUniversity,andtoother
iii
iv Preface
members of his department and of the Department of Foundations of Economic Analysis I for
theirreception(Josune,Miguel,Fede,Luis,Elena,Javier,...).Finally,IamalsoindebtedtoJordi
forbeingmyhostduringmystayatUniversitatAutònomadeBarcelona.
I have to write some lines about my officemates, Rosa and Julio. They have been a great
supportwithmyproblemswiththeliterature,andtheyhavealwaysbeenthereforanyrequest.
Wehavespentalotoftimeinour“warm”officeanditwouldnothavebeenthesamewithout
theirfriendship.
IdonotwanttoforgetthepeoplefromthegroupofGaliciangametheoristsandfromtheDe-
partmentofStatisticsandOperationsResearchatUniversityofSantiagodeCompostela. They
have been an important support during my PhD years. I also want to thank all the other PhD
students of the Faculty of Mathematics for our funny “pachangas” and for the pleasant coffee
breaksanddinners. ThankstoTere,Marco,Bea,Carlitos,Miguel,Cris,Juanjo,...
Ialsowanttorecallallmyfriends,Silvia,Bea,Mirian,Sol,Rosa,Trini,Martín,...thankyou
foryourfriendshipandforkeepingmeintotherealworld.
OneimportantpersonwhowasclosetomefromthebeginningofmyBacheloruntilnow,is
Yoli. Iamdeeplyindebtedtoherforanuncountablesetofreasons. WithoutherIwouldnotbe
inthispointofmylife. Thisthesisisalsoyours,Yoli.
Finally, the most important support comes from my parents and from my brother. They
taughtmethemostimportantlessonsofthelife,thingsthatnobodycouldteachmebetterthan
them. Muchasgraciasporhaberestadoamiladotodoestetiempo.
ManuelAlfredoMosqueraRodríguez
SantiagodeCompostela,October2006
Contents
Preface iii
Contents v
Notations vii
I OperationsResearchGames 1
Introduction 3
SHORTBIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1 Coalitionalmanipulation&centralizedinventorymanagement 7
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Coalitionalmanipulationininventorygames . . . . . . . . . . . . . . . . . . . . . . 8
1.3 TheMainResult . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Sharingcostsinhighways: agametheoreticalapproach 15
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Highwayproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Naturalsharingcostrulesforhighwaygames . . . . . . . . . . . . . . . . . . . . . 20
2.4 Thenucleolusofhighwaygames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3 Proportionateflowshopgames 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Proportionateflowshopproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3 Cooperationinproportionateflowshops . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4 Proportionateflowshopgames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
II CautiousBehavior 73
Introduction 75
SHORTBIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4 Characterizingcautiouschoice 77
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2 Acharacterizationofthesetofmaximinactions . . . . . . . . . . . . . . . . . . . . 79
4.3 Proofofthecharacterizationtheorem. . . . . . . . . . . . . . . . . . . . . . . . . . . 81
v
vi Contents
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5 Anoteonaxiomatizationsofprotectiveness 91
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2 Themodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Axiomatizationsofprotectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4 Logicalindependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
ResumenenCastellano 107
BIBLIOGRAFÍADELRESUMEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
AuthorIndex 117