International Series in Operations Research & Management Science Pierre-Olivier Pineau Simon Sigué Sihem Taboubi Editors Games in Management Science Essays in Honor of Georges Zaccour International Series in Operations Research & Management Science Volume 280 SeriesEditor CamilleC.Price DepartmentofComputerScience,StephenF.AustinStateUniversity, Nacogdoches,TX,USA AssociateEditor JoeZhu FoisieBusinessSchool,WorcesterPolytechnicInstitute,Worcester,MA,USA FoundingEditor FrederickS.Hillier StanfordUniversity,Stanford,CA,USA Moreinformationaboutthisseriesathttp://www.springer.com/series/6161 Pierre-Olivier Pineau • Simon Sigué Sihem Taboubi Editors Games in Management Science Essays in Honor of Georges Zaccour 123 Editors Pierre-OlivierPineau SimonSigué ChairinEnergySectorManagement FacultyofBusiness HECMontréalEnergySectorManagement AthabascaUniversity Montréal,QC,Canada Athabasca,AB,Canada SihemTaboubi DepartmentofMarketing GERADandHECMontréal Montréal,QC,Canada ISSN0884-8289 ISSN2214-7934 (electronic) InternationalSeriesinOperationsResearch&ManagementScience ISBN978-3-030-19106-1 ISBN978-3-030-19107-8 (eBook) https://doi.org/10.1007/978-3-030-19107-8 ©SpringerNatureSwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This volume is written to mark the 60th birthday of Professor Georges Zaccour. The contributors, who are either former Ph.D. students or successful research collaborators and friends of Professor Zaccour, want to take this opportunity to acknowledgehiscontributionsandtohonorhismanyscientificachievements. It would be unrealistic and inadvisable to attempt to give a full account of Georges Zaccour’s scientific achievements in a book preface. We hope, however, thatthefewpointsbelowwillhelpthereaderappreciatetheextentofhiscontribu- tiontoscience. Allthingsconsidered,GeorgesZaccourisoneofthemostprolificscholarsofhis generation in the fields of operations research and management science. His work covers theoretical developments as well as applications of dynamic optimization anddynamicgamesinvariousfieldsincludingeconomics,energy,theenvironment, marketing, and supply chain management. His work is published regularly in top- ranked journals and is funded by the Natural Sciences and Engineering Research Council of Canada and the Social Sciences and Humanities Research Council of Canada. His publications include 4 books, 14 edited volumes, over 150 refereed journalarticles,and24chaptersineditedbooks.HisGoogleScholarprofilereflects theimpactsofhiscontributionsinhisresearchfields(closeto6000citationsandan hindicatorof39).Amongmanyscientificdistinctionsandawards,GeorgesZaccour isafellowoftheRoyalSocietyofCanadaandarecipientofthe2018IsaacsAward forhisoutstandingcontributiontothetheoryandapplicationofdynamicgames.A completelistofhispublicationsisincludedinthisbook. Service to and leadership in the scientific community have always been a top priority for Georges Zaccour. Among other things, he is the editor in chief of Dynamic Games and Applications, and the associate editor of International Game Theory Review, Environmental Modeling & Assessment, Computational ManagementScience,andINFOR,andhesitsontheeditorialboardsofseveralother prestigiousjournalsinvariousfields.HeistheholderoftheChairinGameTheory and Management at HEC Montréal and a former president of the International SocietyofDynamicGames(ISDG,2002–2006).Heisalsoaformerdirectorofthe GroupforResearchinDecisionAnalysis(GERAD,2001–2005),aworld-renowned v vi Preface researchcenterinoperationsresearchandmanagementsciencethatbringstogether severaluniversitiesinMontréal. But perhaps Georges Zaccour’s most significant contribution to science is his dedication to, passion for, and unparalleled skill at training graduate students and hisabilitytohelpthemdevelopintothrivingresearchers.Thankstohisoutstanding work in this area and his capacity to create a blossoming research environment, the future of research in the field of differential games and their applications in management science has never been as promising as it is today. Over the years, ProfessorZaccourhascreatedascientificfamilyofmorethan35Ph.D.andpost-doc graduates, who are established in seven different countries across four continents. Thisfamilywillsoongrow,withtheadditional15studentscurrentlyworkingunder hissupervision. ProfessorGeorgesZaccourwithhisPh.D.students.Fromlefttoright:Pierre-OlivierPineau,Sihem Taboubi,SimonSigué.9thISDGSymposium,Adelaide,SouthAustralia,December18–21,2000. We, the editors of this volume and the organizers of the 11th Workshop on DynamicGamesandManagementScience(Montréal,October,24–25,2019),being held in his honor, were among Professor Zaccour’s first Ph.D. students (2000, 1999,and2002,respectively).Wehavetheprivilegeofpubliclyacknowledgingthe extraordinary support and mentorship he has provided us, first during our training at HEC Montréal, and later in our respective careers and personal lives. What we have become, we owe to him. It goes without saying that we are very proud to be partofProfessorZaccour’smultigenerationalscientificfamily,whichincludesnot Preface vii only his extensive network of distinguished collaborators and friends worldwide, but also, as of this volume, his daughter, Suzanne Zaccour. Suzanne, the youngest contributortothiscollection,ispursuingaPh.D.withtheFacultyofLawatOxford University.WithMichèleBreton,shehasco-authoredachapterthatopensdoorsto newapplicationsofmanagementscienceinthefieldoflaw. Contentsofthe Book This book collects 21 chapters reviewed according to international journal stan- dards. The chapters cover theoretical developments in game theory and present a broad spectrum of their applications in management science. These applications include such areas as cyber defense, energy, and environmental management, healthcaremanagement,marketing,andsupplychainmanagement. Wehavedividedthevolumeintothreeparts.PartI,composedofsixchapters,is dedicatedtoMarketingandSupplyChainGames.InChap.1,S.JørgensenandS.P. Siguéinvestigateadifferentialgamethattakesplaceinaduopolisticmarketwhere firmscontroltheiradvertisingandpricingdecisions.Anovelaspectoftheirstudyis thattheyintroducepriceasanadditionalinstrumentusedbycompetingfirmsinthe commonly used Lanchester model, which originally solely captured the effects of advertisingcompetitionontheevolutionofthefirms’marketshares.InChap.2,G. Martín-HerránandS.Taboubistudythepricingofoptionalcontingentproducts(i.e., a set of products that includes one that is useless without the other) and compare prices and profits when these products are sold by the same company or by two separatefirmslinkedbytheinterdependencyoftheirproductdemand.Theirstudy provides an interesting “logical experimental” perspective on marketing modeling andgametheory,twoareasofexpertiseofProfessorZaccour.InChap.3,S.Karray conducts one of the first studies to examine the efficiency of rebate programs in marketing channels where competition is considered at both the manufacturer and retailer levels. Rebate programs are price discounts that consumers acquire by purchasing a product at an initial period and that they then use on the next purchasing occasion. The author uses a two-period game, where manufacturers decide in the first period whether or not to implement a rebate program, while retailers react by fixing the rebate level and the price to consumers. Retailers also set the retail prices in period 2 by taking into account the decisions made in the first period. Backward induction is used to solve the games under three scenarios, in which the rebate program can be implemented or not by one or both manufacturers in the distribution channel. In Chap. 4, L. Lambertini deals with the issue of channel coordination through the use of two-part tariffs. These are price mechanisms that manufacturers can use in order to allow a decentralized channel to replicate the results of a vertically integrated one. The author extends the study of Zaccour (2008), on the efficiency of such mechanisms in a dynamic setting, by introducing competition both upstream and downstream. In Chap. 5, O.Rubelstudiescontractualagreementsintheeventofmajorcrisiseventsfroma viii Preface channel’sperspective.Heusesastochasticdifferentialgameinabilateralmonopoly to examine the impact of a product recall on the pricing strategies and profits of both firms. The author investigates whether vendor agreements, which are signed before any unit is sold, could aggravate the double-marginalization problem in the channel, for two recall cost structures. In Chap. 6, P. De Giovanni and T. S. Gencinvestigateaclosed-loopsupplychainwherememberscanimplementeithera traditionalwholesalepricingcontractorarevenue-sharingcontract.Unlikeprevious studies,wherethereturnrateissolelyaffectedbythemanufacturer’sgreenefforts, the authors introduce the retail prices set by the retailer into the dynamics, and demonstrate that this variable plays a key role in identifying the best contract for achievingcoordinationandforreachingenvironmentalobjectives. PartIIcontainssixchaptersdedicatedtoResourcesGames,whichalsoincludes environmental and climate topics. In Chap. 7, O. Bahn and A. Haurie formulate a steady-state game model with two types of production economy (“dirty” and “clean”) and two types of emission-reduction technology (investment in carbon capture and sequestration, and a technology of direct air capture). Their model presents the results of negotiations among different coalitions of countries in managing a net-zero Greenhouse Gas (GHG) emissions regime. The authors use it to compute and compare various environmental and economic indicators (i.e., GHG emissions, capital stocks, labor allocation, consumption) obtained under a Nash game and a cooperative game. In Chap. 8, H. Dawid, R. F. Hartl, and P. M. Kort build a general dynamic model for a firm that uses as an input in its production process an energy that can be delivered either conventionally or by building a stock of green energy capital. The authors analyze variations of this model and examine the impacts on the results. A key element is their explicit modeling of the positive side effect of investing in green energy. This is done to capture the fact that firms investing in green energy are positioning themselves as “greenfirms,”whichhelpsenhance theimpactoftheiradvertisingeffortsontheir goodwillandondemand.InChap.9,D.TasneemandH.Benchekrounreviewthe experimental literature that analyzes the behavior of agents in dynamic common- pool resource games (such as fisheries, forestry, and water). The authors propose a classification of this literature into three groups: studies that compare behavior to predictions of cooperative and noncooperative theoretical benchmarks in the presenceofdynamicexternalities;studiesthataimtofindbehavioralsupportforthe useofspecifictypesofstrategies;andstudiesthatexaminebehaviorsinacontinuous timesetting.InChap.10,D.ClaudeandM.Tidballstudyverticalexternalitiesand strategic delegation, a topic that links two fields of research to which Professor Zaccour has made significant contributions: interactions in marketing channels, andenvironmentalandresourceeconomics.Theauthorsconsideraverticalmarket structurewithanupstreammonopoly,whichfixestheinputprice,andadownstream quantitycompetition,wherefirmsgeneratepollutionemissionswhentheyprocess theintermediateproductintoafinalgood.Theycomputeandcomparetheresultsof theirmodelundertwoscenarios,dependingonwhethertheupstreammonopolistis able to pre-commit to a fixed input price or whether it relies on a flexible pricing scheme. In Chap. 11, J. de Frutos and G. Martín-Herrán use a linear-quadratic Preface ix transboundary pollution game to illustrate how nonlinear incentive strategies can sustain an agreement over time. The authors use a less restrictive definition of incentive equilibria with respect to the existing literature, in the sense that they look for an incentive strategy equilibrium that allows the pollution stock under a noncooperativemodeofplaytobecloseenough,butnotnecessarilyidentical,toits valueundercooperation.Theauthorscomparetheincentiveequilibriumstrategies, theircredibility,andtheplayers’payoffunderopen-loopandMarkovianstrategies. InChap.12,F.J.AndréandL.M.Castrosurveytheliteratureonemissiontrading undermarketpower.Theydevelopaunifyingtwo-periodmodelthatallowsthemto replicate some of the main results in this literature and to analyze the relationship between permit prices and the degree of competition in the output and emissions markets for different market structures (depending on which is the mainstream market). Finally, Part III deals with Social Games. It combines nine chapters on various topics related to health, security, social norms, the law, etc., including some theoretical developments in game theory. In Chap. 13, M. Breton and S. Zaccour launch a new and original conversation between the law and game theory on the personhoodstatusofenvironmentalentities.Bygrantingpersonhoodstatustoariver sufferingfromafirm’spollutingactivities,theauthorsallowtherivertobecomean activedownstreamplayerinacooperativegame.Theyshowthatcooperationwith environmentalentitieshavingapersonhoodstatusmaybepreferabletoalternative solutions such as laissez-faire, government regulation, and noncooperative or cooperativesolutionsinvolvinginterestedparties. In Chap. 14, N. Van Long introduces the concept of a feedback Kant-Nash equilibrium in a discrete time model of resource exploitation. The author revisits thewell-knowndynamicmodelofthetragedyofthecommons,whereheconsiders a subset of Kantian agents guided by a moral norm. This norm allows them to explain their actions according to different rules than those used by rational agents (i.e., Nashians). One of the main results obtained is that, even without external punishment for violations of social norms, if a sufficiently large fraction of the population consists of Kantian agents, the tragedy of the commons can be substantiallyattenuated. In Chap. 15, E. Billette de Villemeur and P. Pineau investigate the double prisoner’s dilemma resulting from the fact that some individuals continue to consume increasing amounts of oil, despite their high price, while at the same time, environmental militants oppose production in the oil industry. The authors examine the impacts on the individual and collective outcomes of two sets of choices: being an environmental militant or not, and adopting for a frugal level of energy consumption or not. One of their main results indicates that the highest collective outcome is obtained when frugal behavior is adopted but militancy is avoided. This result allows them to conclude that effective environmental action shouldavoidopposingoilsupplysources,whileencouragingconsumerstobecome morefrugal. In Chap. 16, F. Cabo, A. Garcia-Gonzales, and M. Molpeceres-Abella study compliancewithsocialnormsthatareoptimallyestablishedbyabenevolentcentral