A-potential function and a non-cooperative foundation for the Solidarity value

Xu, Genjiu; Dai, Han; Hou, Dongshuang; Sun, Haitao

doi:10.1016/j.orl.2015.12.002

Cited by 14 publications

(8 citation statements)

References 13 publications

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“…On the other hand, when C = C N , because satisfies efficiency and quasi-balanced contributions for the grand coalition, then by Theorem 4.2 in Xu et al (2016), we can obtain…”

Section: Theorem 8 a Coalitional Value Satisfies Efficiency Additivit...mentioning

confidence: 96%

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Two-step Shapley-solidarity value for cooperative games with coalition structure

Zou

Uetz

et al. 2022

OR Spectrum

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This paper proposes an alternative for the two-step Shapley value for cooperative games with coalition structure that has earlier been proposed by Kamijo. The value is based on the idea that within a union of players, worth should be distributed based on the solidarity principle. Specifically, we propose a two-step Shapley-solidarity value, in which the surplus of a union’s Shapley value in the quotient game is distributed equally among the union’s members, and players obtain the solidarity value of the respective subgame within their union. We provide an intuitive procedural characterization for this value and give three axiomatizations to pinpoint the differences to comparable values.

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“…On the other hand, when C = C N , because satisfies efficiency and quasi-balanced contributions for the grand coalition, then by Theorem 4.2 in Xu et al (2016), we can obtain…”

Section: Theorem 8 a Coalitional Value Satisfies Efficiency Additivit...mentioning

confidence: 96%

“…It requires that any two players must have the same impacts on mutual payoff when one of them departs from the game. Subsequently, Xu et al (2016) introduce quasi-balanced contributions to verify that the solidarity value is the unique efficient value satisfying this property.…”

Section: Quasi-balanced Contributions For Grand Coalitionmentioning

confidence: 99%

Two-step Shapley-solidarity value for cooperative games with coalition structure

Zou

Uetz

et al. 2022

OR Spectrum

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“…Later on, Kamijo and Kongo [14] showed that both the egalitarian value and the solidarity value satisfy the balanced cycle contributions property and presented general axiomatizations of the above two values. Xu et al [32] introduced an Apotential function and deduced the recursive formula of the Solidarity value. They also characterized the Solidarity value by the quasi-balanced contributions property.…”

mentioning

confidence: 99%

Extension of generalized solidarity values to interval-valued cooperative games

Li¹,

Ye²,

Wei³

2020

Journal of Industrial &Amp; Management Optimization

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The main purpose of this paper is to extend the concept of generalized solidarity values to interval-valued cooperative games and hereby develop a simplified and fast approach for solving a subclass of interval-valued cooperative games. In this paper, we find some weaker coalition monotonicity-like conditions so that the generalized solidarity values of the α-cooperative games associated with interval-valued cooperative games are always monotonic and non-decreasing functions of any parameter α ∈ [0, 1]. Thereby the intervalvalued generalized solidarity values can be directly and explicitly obtained by computing their lower and upper bounds through only using the lower and upper bounds of the interval-valued coalitions' values, respectively. The developed method does not use the interval subtraction and hereby can effectively avoid the issues resulted from it. Furthermore, we discuss the effect of the parameter ξ on the interval-valued generalized solidarity values of interval-valued cooperative games and some significant properties of interval-valued generalized solidarity values.2010 Mathematics Subject Classification. Primary: 91A12.

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“…It is verified in [120] that the solidarity value is the unique efficient value satisfying this property.…”

Section: Axiomatizations Of Valuesmentioning

confidence: 83%

“…It requires that any two players must have the same impacts on mutual payoff when one of them departs from the game. Subsequently, Xu et al [120] introduced quasi-balanced contributions axiom. The value ϕ is said to satisfy…”

Section: Axiomatizations Of Valuesmentioning

confidence: 99%

Solutions for cooperative games with restricted coalition formation and almost core allocations

Zhou¹

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A-potential function and a non-cooperative foundation for the Solidarity value

Cited by 14 publications

References 13 publications

Two-step Shapley-solidarity value for cooperative games with coalition structure

Two-step Shapley-solidarity value for cooperative games with coalition structure

Extension of generalized solidarity values to interval-valued cooperative games

Solutions for cooperative games with restricted coalition formation and almost core allocations

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