Coalitional Network Games
21 Pages
English
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Coalitional Network Games

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21 Pages
English

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Niveau: Supérieur, Doctorat, Bac+8
Coalitional Network Games † Preliminary version Jean-Franc¸ois Cauliera, Ana Mauleonb,c, Vincent Vannetelboschc aCEREC, Facultes universitaires Saint-Louis, Boulevard du Jardin Botanique 43, B-1000 Brussels, Belgium. bFNRS and CEREC, Facultes universitaires Saint-Louis, Boulevard du Jardin Botanique 43, B-1000 Brussels, Belgium. cFNRS and CORE, Universite catholique de Louvain, 34 voie du Roman Pays, B-1348 Louvain-la-Neuve, Belgium. December 11, 2009 Abstract Coalitional network games are real-valued functions defined on a set of play- ers (the society) organized into a network and a coalition structure. The network specifies the nature of the relationship each individual has with the other individ- uals and the coalition structure specifies a collection of groups among the society. Coalitional network games model situations where the total productive value of a network among players depends on the players' group membership. These games thus capture the public good aspect of bilateral cooperation, i.e., network games with externalities. After studying the specific structure of coalitional networks, we propose an allocation rule under the perspective that players can alter the coalitional network structure. This means that the value of all potential alternative coalitional networks can and should influence the allocation of value among players in any given coalitional network structure.

  • games

  • group

  • coalitional

  • cooperative game

  • can alter

  • networks

  • coalition

  • players depends

  • all players


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CoalitionalNetworkGamesPreliminaryversionJean-Franc¸oisCauliera,AnaMauleonb,c,VincentVannetelboschcaCEREC,Faculte´suniversitairesSaint-Louis,BoulevardduJardinBotanique43,B-1000Brussels,Belgium.bFNRSandCEREC,Faculte´suniversitairesSaint-Louis,BoulevardduJardinBotanique43,B-1000Brussels,Belgium.cFNRSandCORE,Universite´catholiquedeLouvain,34voieduRomanPays,B-1348Louvain-la-Neuve,Belgium.December11,2009AbstractCoalitionalnetworkgamesarereal-valuedfunctionsdefinedonasetofplay-ers(thesociety)organizedintoanetworkandacoalitionstructure.Thenetworkspecifiesthenatureoftherelationshipeachindividualhaswiththeotherindivid-ualsandthecoalitionstructurespecifiesacollectionofgroupsamongthesociety.Coalitionalnetworkgamesmodelsituationswherethetotalproductivevalueofanetworkamongplayersdependsontheplayers’groupmembership.Thesegamesthuscapturethepublicgoodaspectofbilateralcooperation,i.e.,networkgameswithexternalities.Afterstudyingthespecificstructureofcoalitionalnetworks,weproposeanallocationruleundertheperspectivethatplayerscanalterthecoalitionalnetworkstructure.Thismeansthatthevalueofallpotentialalternativecoalitionalnetworkscanandshouldinfluencetheallocationofvalueamongplayersinanygivencoalitionalnetworkstructure.JELclassification:A14,C70.Keywords:Networks,CoalitionStructures,Externalities.CorrespondingauthorsE-mailaddresses:caulier@fusl.ac.be(Jean-Franc¸oisCaulier),mauleon@fusl.ac.be(AnaMauleon),vincent.vannetelbosch@uclouvain.be(VincentVannetel-bosch).
1IntroductionConsidersituationswhereindividualsorplayersfromasocietynegotiatebilaterallytocooperate.Insuchcasesindividualsareconnectedinsomenetworkrelationship.Consideratthesametimethattheindividualsinvolvedinanetworkrelationshipbelongtogroups,clubs,orcoalitions.Manyapplicationsareinstancesofsuchcoop-erativerelationships,rangingfromfriendshipsamongpeoplebelongingtodifferentcommunities,tocommunicatinginformationaboutjobopportunitiesamongpeoplewithdifferentskills,tostrategicalliancesbetweenfirmsfromdifferentgroups,tobilateralfreetradeagreementsamongcountriesfromdifferentfreetradezones.Acommonfeatureofthesesituationsisthatthewayinwhichplayersareconnectedtoeachotherandthewaytheyareorganizedinmutuallydisjointgroupsdeterminethetotalproductivityorvaluegeneratedbythesociety.Thistotalproductivityorvaluemaybecapturedbyareal-valuedfunctiondefinedonstructuresconsistingofanetworkandacollectionofdisjointcoalitions.Suchstructuresarenamedcoalitionalnetworks,andthereal-valuedfunctionsdefinedoncoalitionalnetworksarenamedcoalitionalnetworkgames(seeCaulier,MauleonandVannetelbosch,2009).Inthisarticleweexaminehowthetotalvaluegeneratedbyplayerscooperatingthroughnetworksandgroupsshouldbeallocatedortransferredamongplayers.Thisissueappearstobeimportantbothintermsofequity:whatisaplayer’sfairsharetohercooperativeparticipation;andalsointermsofplayers’incentivestocooperate:whatistheplayer’sprospecttocooperateinaparticularcoalitionalnetwork?Puttogetherthesetwoquestionscanbesummarizedbythefollowingone:whatkindofcoalitionalnetworkstructurecanweexpecttoform?Cooperativegametheoryliteratureprovidesrichaxiomaticfoundationsontheallocationofvaluebyexaminingwhichproductivevalueisgeneratedbyeachpos-siblecoalitionofplayers.Incoalitionalnetworkgames,primitiveinformationsaredifferentfromcooperativegametheorywithrespecttotwoaspects.First,thevaluegeneratedbyagroupofplayersdependsnotonlyontheidentitiesoftheplayersbutalsoonthelinksconnectingtheplayers.Second,wecannotexaminethevaluegeneratedbyagroupofplayersindependentlyofhowareorganizedtheotherplay-ers.Incooperativegametheory,thevaluegeneratedbyagrouporcoalitionofplayersisindependentofthecoalitionstructureformedbytheotherplayers.Inoursetting,avalueisgeneratedbythewholesocietyanddependonhowtheplayers1