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Procedural and optimization implementation of the weighted ENSC value

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Abstract

The main purpose of this article is to introduce the weighted ENSC value for cooperative transferable utility games which takes into account players’ selfishness about the payoff allocations. Similar to Shapley’s idea of a one-by-one formation of the grand coalition [Shapley (1953)], we first provide a procedural implementation of the weighted ENSC value depending on players’ selfishness as well as their marginal contributions to the grand coalition. Second, in the spirit of the nucleolus [Schmeidler (1969)], we prove that the weighted ENSC value is obtained by lexicographically minimizing a complaint vector associated with a new complaint criterion relying on players’ selfishness.

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Notes

  1. Alternative scenarios of the Shapley value have been provided in the literature by, for example, Felsenthal and Machover (1996).

  2. Among others, the results of Guth et al. (1982), Forsythe et al. (1994), Nowak et al. (2000), and Chen et al. (2014) reinforce this view.

  3. Recently, an interesting characterization of the ENSC value was proposed by Béal et al. (2016) using the axiom of balanced collective contributions together with the classical axiom of efficiency.

  4. Davis and Maschler (1965) introduced the complaint of a coalition based on the excess criterion to determine the kernel of TU-games.

  5. This assumption is reasonable in many real-life situations such as, for example, the constitution of an information exchange forum among the firms using the common chemical substance under the new European legislation REACH (Dehez and Tellone 2013).

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xan, China

    Dongshuang Hou, Panfei Sun & Hao Sun

  2. Université Côte d’Azur, CNRS, GREDEG, Côte d’Azur, France

    Aymeric Lardon

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  1. Dongshuang Hou
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  2. Aymeric Lardon
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  3. Panfei Sun
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  4. Hao Sun
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Correspondence to Aymeric Lardon.

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D. Hou: The first author acknowledges financial support by National Science Foundation of China (NSFC) through Grant No. 71871180, 71601156, 71571140, 71571143.

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Hou, D., Lardon, A., Sun, P. et al. Procedural and optimization implementation of the weighted ENSC value. Theory Decis 87, 171–182 (2019). https://doi.org/10.1007/s11238-019-09697-5

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