A Procedure for Computing the f-Nucleolus of a Cooperative Game

Wallmeier, Eugen

doi:10.1007/978-3-642-45567-4_21

Cited by 5 publications

(3 citation statements)

References 4 publications

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“…For completeness, we present (without proof) a characterization of weighted prenucleoli in terms of balanced collections. It is a slight generalization of the charac-terization given by Wallmeier (1984) for q-prenucleoli with monotone nondecreasing and symmetric (i.e. q(S) = q(|S|) for all S ∈ N ) weight function, that, in turn is a straightforward generalization of Kohhlberg's (1971) criterion for the standard prenucleolus.…”

Section: (13)mentioning

confidence: 99%

Weighted nucleoli and dually essential coalitions

Solymosi

2019

Int J Game Theory

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We consider linearly weighted versions of the least core and the (pre)nuceolus and investigate the reduction possibilities in their computation. We slightly extend some well-known related results and establish their counterparts by using the dual game. Our main results imply, for example, that if the core of the game is not empty, all dually inessential coalitions (which can be weakly minorized by a partition in the dual game) can be ignored when we compute the per-capita least core and the per-capita (pre)nucleolus from the dual game. This could lead to the design of polynomial time algorithms for the per-capita (and other monotone nondecreasingly weighted versions of the) least core and the (pre)nucleolus in specific classes of balanced games with polynomial many dually essential coalitions.

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Section: (13)mentioning

confidence: 99%

Weighted nucleoli and dually essential coalitions

Solymosi

2019

Int J Game Theory

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“…To distinguish the cardinality of coalitions by constructing the formula of excess, f-excess and f-nucleolus are proposed by Wallmeier [9] as follows.…”

Section: Definitionmentioning

confidence: 99%

“…Tarashnina [8] developed the simplified modified nucleolus (SMnucleolus) to simplify the structure of M-nucleolus, and clarified the question in what ratio the constructive and the blocking powers are considered. In order to distinguish the cardinality of coalitions in the excess formulae, Wallmeier [9] defined the f-excess based on a non-increasing function, and then f-nucleolus is intro-duced detailedly. Moreover, f-nucleolus is extended to the flow games by Kern and Paulusma [10].…”

Section: Introductionmentioning

confidence: 99%

The G-nucleolus for fuzzy cooperative games

Lin

Zhang

2014

Journal of Intelligent &Amp; Fuzzy Systems

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In this study, the G-nucleolus of fuzzy cooperative games is proposed based on the G-excess of fuzzy coalitions. The G-nucleolus considers not only the constructive and the blocking powers, but also the size of fuzzy coalitions. Moreover, we show that the G-nucleolus is reasonable, and coincides with the SM-nucleolus when the function f is equal to 1 for each fuzzy coalition. The G-nucleolus can be obtained by calculating the f-nucleolus of a constant-sum fuzzy cooperative game. We prove that G-nucleolus belong to the non-empty precore of the corresponding constant-sum fuzzy cooperative game. Finally, some linear programming models are employed to generate the G-nucleolus effectively.

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A Modified Kohlberg Criterion and a Nonlinear Method to Compute the Nucleolus of a Cooperative Game

Kido¹

2008

Taiwanese J. Math.

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A Procedure for Computing the f-Nucleolus of a Cooperative Game

Cited by 5 publications

References 4 publications

Weighted nucleoli and dually essential coalitions

Weighted nucleoli and dually essential coalitions

The G-nucleolus for fuzzy cooperative games

A Modified Kohlberg Criterion and a Nonlinear Method to Compute the Nucleolus of a Cooperative Game

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