一类优先联盟内有限制的具有联盟结构的合作对策
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摘要
结合具有联盟结构的合作对策和具有权限结构的合作对策,考虑了一类优先联盟内有限制的合作对策.在这类合作对策中,局中人结成一些优先联盟参与合作,而各优先联盟内部具有层级组织结构,其中某些局中人对其他人的行动具有否决权.定义了这类合作对策的一个解,该解是Owen值的推广.证明了其公理化结论,最后通过一个算例说明这类合作对策在收益分配问题中的应用.
A new model of cooperative game with coalition structure and restrictions within priori unions is discussed in this paper by combining games with coalition structures and games with permission structures.In this kind of cooperative game,players are partitioned into a coalition structure and there exists hierarchical organization within every priori union,which means that some players have veto power over the actions undertaken by other players.A value is defined for these games which generalizes the Owen value.An axiomatic characterization of this value is provided and a numerical example is given to illustrate the application of the proposed cooperative game in revenue allocation problem.
A new model of cooperative game with coalition structure and restrictions within priori unions is discussed in this paper by combining games with coalition structures and games with permission structures.In this kind of cooperative game,players are partitioned into a coalition structure and there exists hierarchical organization within every priori union,which means that some players have veto power over the actions undertaken by other players.A value is defined for these games which generalizes the Owen value.An axiomatic characterization of this value is provided and a numerical example is given to illustrate the application of the proposed cooperative game in revenue allocation problem.
引文
[1]Owen G.Values of games with a priori unions[M].Mathematical Economics and Game Theory.Springer Berlin Heidelberg,1977:76-88.
[2]Vazquez-Brage M,GarcíI,Carreras F.The Owen value applied to games with graph-restricted communication[J].Games and Economic Behavior,1996,12(1):42-53.
[3]Meng F Y,Zhang Q.Cooperative games on convex geometries with a coalition structure[J].Journal of Systems Science and Complexity,2012,25(5):909-925.
[4]Meng F Y,Chen X H,Zhang Q.A coalitional value for games on convex geometries with a coalition structure[J].Applied Mathematics and Computation,2015,266:605-614.
[5]孙红霞,张强.具有联盟结构的限制合作博弈的限制Owen值[J].系统工程理论与实践,2013,33(4):981-987.Sun H X,Zhang Q.Restricted Owen value in restricted games with coalition structure[J].Systems Engineering-Theory&Practice,2013,33(4):981-987.
[6]Khmelnitskaya A.Values for games with two-level communication structures[J].Discrete Applied Mathematics,2014,166:34-50.
[7]Van den Brink R,van der Laan G,Moes N.Values for transferable utility games with coalition and graph structure[J].TOP,2015,23(1):77-99.
[8]Gilles R P,Owen G,van den Brink R.Games with permission structures:The conjunctive approach[J].International Journal of Game Theory,1992,20(3):277-293.
[9]Van den Brink R,Gilles R P.Axiomatizations of the conjunctive permission value for games with permission structures[J].Games and Economic Behavior,1996,12(1):113-126.
[10]Gilles R P,Owen G.Cooperative games and disjunctive permission structures[M].Tilburg,the Netherlands:Tilburg University,1999.
[11]Van den Brink R,Dietz C.Games with a local permission structure:Separation of authority and value generation[J].Theory and Decision,2014,76(3):343-361.
[12]Gallardo J M,Jimenez N,Jimenez-Losada A,et al.Games with fuzzy permission structure:A conjunctive approach[J].Information Sciences,2014,278:510-519.
[2]Vazquez-Brage M,GarcíI,Carreras F.The Owen value applied to games with graph-restricted communication[J].Games and Economic Behavior,1996,12(1):42-53.
[3]Meng F Y,Zhang Q.Cooperative games on convex geometries with a coalition structure[J].Journal of Systems Science and Complexity,2012,25(5):909-925.
[4]Meng F Y,Chen X H,Zhang Q.A coalitional value for games on convex geometries with a coalition structure[J].Applied Mathematics and Computation,2015,266:605-614.
[5]孙红霞,张强.具有联盟结构的限制合作博弈的限制Owen值[J].系统工程理论与实践,2013,33(4):981-987.Sun H X,Zhang Q.Restricted Owen value in restricted games with coalition structure[J].Systems Engineering-Theory&Practice,2013,33(4):981-987.
[6]Khmelnitskaya A.Values for games with two-level communication structures[J].Discrete Applied Mathematics,2014,166:34-50.
[7]Van den Brink R,van der Laan G,Moes N.Values for transferable utility games with coalition and graph structure[J].TOP,2015,23(1):77-99.
[8]Gilles R P,Owen G,van den Brink R.Games with permission structures:The conjunctive approach[J].International Journal of Game Theory,1992,20(3):277-293.
[9]Van den Brink R,Gilles R P.Axiomatizations of the conjunctive permission value for games with permission structures[J].Games and Economic Behavior,1996,12(1):113-126.
[10]Gilles R P,Owen G.Cooperative games and disjunctive permission structures[M].Tilburg,the Netherlands:Tilburg University,1999.
[11]Van den Brink R,Dietz C.Games with a local permission structure:Separation of authority and value generation[J].Theory and Decision,2014,76(3):343-361.
[12]Gallardo J M,Jimenez N,Jimenez-Losada A,et al.Games with fuzzy permission structure:A conjunctive approach[J].Information Sciences,2014,278:510-519.