一类具有限制联盟结构的合作对策的两阶段Shapley值
|
摘要
讨论一类具有限制联盟结构的合作对策,其中局中人通过优先联盟整体参与大联盟的合作,同时优先联盟内部有合取权限结构限制,利用两阶段Shapley值的分配思想并考虑到权限结构对优先联盟内合作的限制,给出了此类合作对策的解。该解可看做具有联盟结构的合作对策的两阶段Shapley值的推广。证明了该解满足的公理化条件,并验证了这些条件的独立性。
A kind of cooperative games with restricted coalition structure are discussed, in which players participate in the cooperation of the grand coalition through the priori unions as a whole and there are conjunctive permission structures within the priori unions. A solution to this kind of cooperative games is given by using the two-step Shapley value distribution idea and taking into account the limits of permission structure on cooperation within the priori unions. This solution can be seen as a generalization of the two-step Shapley value for games with coalition structures. The axiomatization conditions of the solution are proved, and the independence of these conditions is verified.
A kind of cooperative games with restricted coalition structure are discussed, in which players participate in the cooperation of the grand coalition through the priori unions as a whole and there are conjunctive permission structures within the priori unions. A solution to this kind of cooperative games is given by using the two-step Shapley value distribution idea and taking into account the limits of permission structure on cooperation within the priori unions. This solution can be seen as a generalization of the two-step Shapley value for games with coalition structures. The axiomatization conditions of the solution are proved, and the independence of these conditions is verified.
引文
[1] Owen G.Values of games with a priori unions[A].Henn R,Moeschlin O.Mathematical economics and game theory[C].Springer,Berlin,Heidelberg,1977.76- 88.
[2] Owen G.Modification of the banzhaf-coleman index for games with a priori unions[A].Holler M J.Power,voting,and voting power[C].Physica,Heidelberg,1981.232-238.
[3] Alonso-Meijide J M,Fiestras-Janeiro M G.Modification of the banzhaf value for games with a coalition structure[J].Annals of Operations Research,2002,109(1- 4):213-227.
[4] Kamijo Y.A two-step Shapley value for cooperative games with coalition structures[J].International Game Theory Review,2009,11(2):207-214.
[5] Kongo T.Value of games with two-layered hypergraphs[J].Mathematical Social Sciences,2011,62(2):114-119.
[6] van den Brink R,Khmelnitskaya A,van der Laan G.An Owen-type value for games with two-level communication structure[J].Annals of Operations Research,2016,243(1-2):179-198.
[7] Béal S,Khmelnitskaya A,Solal P.Two-step values for games with two-level communication structure[J].Journal of Combinatorial Optimization,2018,35(2):563-587.
[8] Meng F,Chen X,Zhang Q.A coalitional value for games on convex geometries with a coalition structure[J].Applied Mathematics and Computation,2015,266:605- 614.
[9] Meng F,Zhang Q,Chen X.A value for games on augmenting systems with a coalition structure[J].Operations Research Letters,2016,44(3):324-328.
[10] 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.
[11] 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.
[12] van den Brink R,Gilles R P.Axiomatizations of the conjunctive permission value for games with permission structures[J].Games & Economic Behavior,1996,12(1):113-126.
[13] Shapley L S.A value for n-person games[A].Kuhn H W,Tucker A W.Contributions to the Theory of Games II[C].Princeton University Press,Princeton,1953,28:307-317.第28卷第5期
[2] Owen G.Modification of the banzhaf-coleman index for games with a priori unions[A].Holler M J.Power,voting,and voting power[C].Physica,Heidelberg,1981.232-238.
[3] Alonso-Meijide J M,Fiestras-Janeiro M G.Modification of the banzhaf value for games with a coalition structure[J].Annals of Operations Research,2002,109(1- 4):213-227.
[4] Kamijo Y.A two-step Shapley value for cooperative games with coalition structures[J].International Game Theory Review,2009,11(2):207-214.
[5] Kongo T.Value of games with two-layered hypergraphs[J].Mathematical Social Sciences,2011,62(2):114-119.
[6] van den Brink R,Khmelnitskaya A,van der Laan G.An Owen-type value for games with two-level communication structure[J].Annals of Operations Research,2016,243(1-2):179-198.
[7] Béal S,Khmelnitskaya A,Solal P.Two-step values for games with two-level communication structure[J].Journal of Combinatorial Optimization,2018,35(2):563-587.
[8] Meng F,Chen X,Zhang Q.A coalitional value for games on convex geometries with a coalition structure[J].Applied Mathematics and Computation,2015,266:605- 614.
[9] Meng F,Zhang Q,Chen X.A value for games on augmenting systems with a coalition structure[J].Operations Research Letters,2016,44(3):324-328.
[10] 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.
[11] 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.
[12] van den Brink R,Gilles R P.Axiomatizations of the conjunctive permission value for games with permission structures[J].Games & Economic Behavior,1996,12(1):113-126.
[13] Shapley L S.A value for n-person games[A].Kuhn H W,Tucker A W.Contributions to the Theory of Games II[C].Princeton University Press,Princeton,1953,28:307-317.第28卷第5期