• •

### 联盟缺额合意性与均分不可分贡献值

1. 西北工业大学数学与统计学院 西安 710129
• 收稿日期:2021-09-15 修回日期:2022-01-19 出版日期:2022-04-25 发布日期:2022-06-18
• 通讯作者: 徐根玖,Email:xugenjiu@nwpu.edu.cn.
• 基金资助:
国家重点研发计划(2021YFA1000400),国家自然科学基金(72071159,71671140),国家留学基金(202006290073)资助课题

ZOU Rong, XU Genjiu. Coalitional Gap Desirability and the Equal Allocation of Non-Separable Contributions Value[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(4): 780-790.

### Coalitional Gap Desirability and the Equal Allocation of Non-Separable Contributions Value

ZOU Rong, XU Genjiu

1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129
• Received:2021-09-15 Revised:2022-01-19 Online:2022-04-25 Published:2022-06-18
In this paper, we firstly provide an axiom for solutions of TU games, called the coalitional gap desirability (CGD), by adapting the recent coalitional surplus desirability (Hu, 2019). It is verified that no solution satisfies both the CGD and the classical efficiency except for the trivial situation where there are no more than two players in a cooperative game. We then introduce an adapted axiom by averaging coalitions’ gap, namely the average coalitional gap desirability. The equal allocation of nonseparable contributions value (ENSC value) is axiomatized by this averaged version together with the efficiency and additivity axioms. Finally, the axiomatic results are extended to the weighted ENSC value (Hou, et al., 2019).

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 [1] Shapley L S. A value for n-person games. Contributions to the Theory of Games II, Annals of Mathematics Studies. Princeton:Princeton University Press, 1953, 307-317.[2] Driessen T S H, Funaki Y. Coincidence of and collinearity between game theoretic solutions. OR Spektrum, 1991, 13(1):15-30.[3] Moulin H. The separability axiom and equal-sharing methods. J. Econ. Theory, 1985, 36(1):120-148.[4] Gillies D B. Some theorems on n-person games. PhD Thesis. Princeton:Princeton University Press, 1954.[5] Hu X F, Li D F. The equal surplus division value for cooperative games with a level structure. Group Decis. Negotiat., 2021, 30:1315-1341.[1] Shapley L S. A value for n-person games. Contributions to the Theory of Games II, Annals of Mathematics Studies. Princeton:Princeton University Press, 1953, 307-317.[2] Driessen T S H, Funaki Y. Coincidence of and collinearity between game theoretic solutions. OR Spektrum, 1991, 13(1):15-30.[3] Moulin H. The separability axiom and equal-sharing methods. J. Econ. Theory, 1985, 36(1):120-148.[4] Gillies D B. Some theorems on n-person games. PhD Thesis. Princeton:Princeton University Press, 1954.[5] Hu X F, Li D F. The equal surplus division value for cooperative games with a level structure. Group Decis. Negotiat., 2021, 30:1315-1341. 790 r^3 Z X 342 W[6] Hou D S, Lardon A, Sun P F, et al. Procedural and optimization implementation of the weighted ENSC value. Theory and Decis., 2019, 87:171-182.[7] Zheng X X, Li D F, Liu Z, et al. Willingness-to-cede behaviour in sustainable supply chain coordination. Int. J. Prod. Econ., 2021, 240:108207.[8] Ju Y, Wettstein D. Implementing cooperative solution concepts:A generalized bidding approach. Econ. Theory., 2009, 39(2):307-330.[9] Sun P F, Hou D S, Sun H, et al. Optimization implementation and characterization of the equal allocation of nonseparable costs value. J. Optim. Theory Appl., 2017, 173:336-352.[10] van den Brink R. Null or nullifying players:The difference between the Shapley value and equal division solutions. J. Econ. Theory, 2007, 136:767-775.[11] Chun Y, Park B. Population solidarity, population fair-ranking, and the egalitarian value. Int. J. Game Theory, 2012, 41:255-270.[12] Casajus A, Huettner F. Null, nullifying, or dummifying players:The difference between the Shapley value, the equal division value, and the equal surplus division value. Econom. Lett., 2014, 122:167-169.[13] Ferri`eres S. Nullified equal loss property and equal division values. Theory Decis., 2017, 83:385-406.[14] Kongo T. Similarities in axiomatizations:Equal surplus division value and first-price auctions. Rev. Econ. Des., 2020, 24:199-213.[15] Hwang Y A. Associated consistency and equal allocation of nonseparable costs. Econ. Theory, 2006, 28(3):709-719.[16] Xu G J, van den Brink R, Gerard V D L, et al. Associated consistency characterization of two linear values for TU games by matrix approach. Linear Algebra Appl., 2015, 471:224-240.[17] Hamiache G. Associated consistency and Shapley value. Int. J. Game Theory, 2001, 30(2):279-289.[18] Béal S, Deschamps M, Solal P. Comparable axiomatizations of two allocation rules for cooperative games with transferable utility and their subclass of data games. J. Public Econ. Theory, 2016, 18(6):992-1004.[19] Myerson R B. Conference structures and fair allocation rules. Int. J. Game Theory, 1980, 9(3):169-182.[20] Maschler M, Peleg B. A characterization, existence proof and dimension bounds for the kernel of a game. Pac. J. Math., 1966, 18(2):117-141.[21] Casajus A, Huettner F. Null players, solidarity, and the egalitarian Shapley values. J. Math. Econ., 2013, 49(1):58-61.[22] Malawski M. "Procedural" values for cooperative games. Int. J. Game Theory, 2013, 42(1):305-324.[23] Béal S, Rémila E, Solal P. Axiomatization and implementation of a class of solidarity values for TU-games. Theory and Decis., 2017, 83(1):61-94.[24] Béal S, Rémila E, Solal P. Coalitional desirability and the equal division value. Theory and Decis., 2019, 86(1):95-106.[25] Hu X F. Coalitional surplus desirability and the equal surplus division value. Econom. Lett., 2019, 179:1-4.
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