Proportional Owen value for the coalition structure cooperative game under the incomplete information
YU Xiaohui1, DU Zhiping1, ZHANG Qiang2, ZOU Zhengxing2
1. Logistics School, Beijing Wuzi University, Beijing 101149, China; 2. School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China
Abstract：The incomplete information cooperative game is a kind of cooperative games with unknown characteristic value for some coaltion values. Because the Owen value is used to solve the coalition structure cooperative game under the totally complete information, the cooperation model under the above incomplete information (partially-defined cooperative game) has been unable to apply. In order to solve the partially-defined cooperative game, we defined proportional Owen value. The proportional Owen value is defined on the coalition with known value. Moreover, the total value of big coalition is allocated by two steps, i.e., between an a prior coalition and in a single a prior coalition. The proportional Owen value is different from Owen value, because the allocation rate for the player in a single coalition is based on the contribution rate in their small coalition. The proportional Owen value satisfied individual rationality, and it is a unique value for partially-defined cooperative game satisfying efficiency, linearity, null coalition property and proportionality, and so on. Finally, the proportional Owen value is applied to the supply chain with some players as a whole under the background of one Belt and Road, as an allocation method for the multilevel cooperative problem with incomplete information.
于晓辉, 杜志平, 张强, 邹正兴. 信息不完全下联盟结构合作对策的比例Owen解[J]. 系统工程理论与实践, 2019, 39(8): 2105-2115.
YU Xiaohui, DU Zhiping, ZHANG Qiang, ZOU Zhengxing. Proportional Owen value for the coalition structure cooperative game under the incomplete information. Systems Engineering - Theory & Practice, 2019, 39(8): 2105-2115.
[1] Aumann R J, Dreze J H. Cooperative games with coalition structures[J]. International Journal of Game Theory, 1974, 3(4):217-237. [2] Hu X F, Xu G J, Li D F. The egalitarian efficient extension of the Aumann-Dreze value[J]. Journal of Optimization Theory and Applications, 2019, 181(3):1033-1052. [3] Owen G. Value of games with a priori unions[C]//Henn R, Moesechlin O. Mathematical Economics and Game Theory, Springer-Verlag, 1977. [4] Shapley L S. A value for n-persons games[J]. Annals of Mathematics Studies, 1953, 28:307-318. [5] Hart S, Kurz M. Endogenous formation of coalitions[J]. Econometrica, 1983, 51(4):1047-1064. [6] 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. [7] 王利明, 张强, 陈纲. 一类优先联盟内有限制的具有联盟结构的合作对策[J]. 系统工程理论与实践, 2017, 37(8):2171-2177.Wang L M, Zhang Q, Chen G. A kind of games with coalition structures and restrictions within priori unions[J]. Systems Engineering-Theory & Practice, 2017, 37(8):2171-2177. [8] Meng F Y, Zhang Q, Wang Y. Cooperative fuzzy games with a coalition structure and interval payoffs[J]. International Journal of Computational Intelligence and Applications, 2013, 6:548-558. [9] Xu G J, Sun H. The Myerson value for cooperative games on communication structure with fuzzy coalition[J]. Journal of Intelligent and Fuzzy Systems, 2017, 33(1):27-39. [10] 邹正兴, 张强, 李美苓. 具有结盟限制的合作对策的加权Shapley值[J]. 系统工程理论与实践, 2018, 38(1):145-162.Zou Z X, Zhang Q, Li M L. The weighted Shapley value for games with restricted cooperation[J]. Systems Engineering-Theory & Practice, 2018, 38(1):145-162. [11] Willson S J. A value for partially defined c0ooperative games[J]. International Journal of Game Theory, 1993, 21:371-384. [12] Housman D. Linear and symmetric allocation methods for partially defined cooperative games[J]. International Journal of Game Theory, 2001, 30:377-404. [13] Polkowski L, Araszkiewicz B. A rough set approach to estimating the game value and the Shapley value from data[J]. Fundamenta Informaticae, 2002, 53:335-343. [14] Masuya S, Inuiguchi M. A fundamental study for partially defined cooperative games[J]. Fuzzy Optimistic Decision Making, 2016, 15:281-306.
2019, Vol. 39 
