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The Shapley Value for Upstream Responsibility Games

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  • Radványi, Anna

Abstract

In this paper sharing the cost of emission in supply chains are considered. We focus on allocation problems that can be described by rooted trees, called cost-tree problems, and on the induced transferable utility cooperative games, called upstream responsibility games (Gopalakrishnan et al., 2017). The formal notion of upstream responsibility games is introduced, and the characterization of the class of these games is provided. The Shapley value (Shapley, 1953) is probably the most popular value for transferable utility cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley (1953)’s and Young (1985)’s axiomatizations of the Shapley value are valid on the class of airport games. We extend Dubey's and Moulin and Shenker's results onto the class of upstream responsibility games, that is, we provide two characterizations of the Shapley value for upstream responsibility games.

Suggested Citation

  • Radványi, Anna, 2018. "The Shapley Value for Upstream Responsibility Games," Corvinus Economics Working Papers (CEWP) 2018/06, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2018/06
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    File URL: https://unipub.lib.uni-corvinus.hu/3779/
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    More about this item

    Keywords

    upstream responsibility games; cost sharing; emission; supply chain; shapley value; rooted tree; axiomatization of the shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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