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Operations Research Transactions >

2024 , Vol. 28 >Issue 4: 91 - 100

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2024.04.008

Alternative axiomatic characterization of the efficient compensation solution with applications

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  • 1. School of Management, Shanghai University, Shanghai 200444, China
    2. Shanghai Police College, Shanghai 200137, China

Received date: 2021-02-07

  Online published: 2024-12-20

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, 2024, All rights reserved, without authorization
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Abstract

The compensation solution is one of the important component efficient allocation rules for cycle-free graph game. Béal et al.(2018) proposed and characterized its efficient extension. In this paper, we propose an alternative axiomatic characterization of the efficient compensation solution. We first show that the efficient compensation solution can be characterized by efficiency, relative fairness and fair distribution of surplus. Secondly, we compare this value with other allocation rules through an application example.

Key words： cooperative game; cycle-free graph; efficient compensation solution; fair distribution of surplus

Cite this article

Manchang ZENG, Jiagui ZHAO, Erfang SHAN . Alternative axiomatic characterization of the efficient compensation solution with applications[J]. Operations Research Transactions, 2024 , 28(4) : 91 -100 . DOI: 10.15960/j.cnki.issn.1007-6093.2024.04.008

References

1 BranzeiR,DimitrovD,TijsS.Models in Cooperative Game Theory[M].Berlin:Springer,2008.
2 MyersonR B.Graphs and cooperation in games[J].Mathematics of Operations Research,1977,2(3):225-229.
3 Shapley L S. A value for $n$-person games[M]//Contributions to the Theory of Games Ⅱ, Princeton: Princeton University Press, 1953: 307-317.
4 SlikkerM,van den NouwelandA.Social and Economic Networks in Cooperative Game Theory[M].New York:Springer,2001.
5 ShanE,ZhangG,ShanX.The degree value for games with communication structure[J].International Journal of Game Theory,2018,47,857-871.
6 BéalS,RémilaE,SolalP.Compensations in the Shapley value and the compensation solutions for graph games[J].International Journal of Game Theory,2012,41(1):157-178.
7 van den BrinkR,KhmelnitskayaA,van der LaanG.An efficient and fair solution for communication graph games[J].Economics Letters,2012,117(3):786-789.
8 BéalS,CasajusA,HuettnerF.Efficient extensions of the Myerson value[J].Social Choice and Welfare,2015,45(4):819-827.
9 HuX,LiD,XuG.Fair distribution of surplus and efficient extensions of the Myerson value[J].Economics Letters,2018,165,1-5.
10 Casajus A. An efficient value for TU games with a cooperation structure[EB/OL]. (2006-09-15)[2021-01-23]. https://home.uni-leipzig.de/casajus/texts/effcoval.pdf.
11 ShanE,HanJ,ShiJ.The efficient proportional Myerson values[J].Operations Research Letters,2019,47(6):574-578.
12 LiD L,ShanE.Efficient quotient extensions of the Myerson value[J].Annals of Operations Research,2020,292(1):171-181.
13 HeringsP J J,van der LaanG,TalmanD.The average tree solution for cycle-free graph games[J].Games and Economic Behavior,2008,62(1):77-92.
14 单而芳,谢娜娜,张广.基于平均树值的无圈图博弈有效解[J].运筹与管理,2017,26,24-30.
15 BéalS,CasajusA,HuettnerF.Efficient extensions of communication values[J].Annals of Operations Research,2018,264(1/2):41-56.
16 KangL,KhmelnitskayaA,ShanE,et al.The average tree value for hypergraph games[J].Mathematical Methods of Operations Research,2021,94,437-460.
17 单而芳,曾晗,韩佳玉.无圈超图对策上的有效平均树解[J].系统工程理论与实践,2021,41(3):781-789.
18 DiestelR.Graph Theory[M].New York:Springer-Verlag,2005.
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