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A Characterization of the Shapley Value based on “Equal Excess"

Author

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  • Shin Kobayashi

    (Graduate School of Economics, Waseda University, 1-6-1 Nishiwaseda Shinjuku-ku, Tokyo 169-8050, Japan.)

Abstract

We examine the relationship between the Shapley value and the excess. Defining the excess of player i by summing up the excesses of all the coalitions to which i belongs, we introduce a condition equal excess. Using this condition, we prove that the Shapley value is characterized as a value satisfying the equal excess with respect to a reasonable weight function. This implies that the Shapley value attains the greatest benefits of the least advantaged players.

Suggested Citation

  • Shin Kobayashi, 2021. "A Characterization of the Shapley Value based on “Equal Excess"," Working Papers 2120, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:2120
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Shapley value; Equal excess; Difference principle; Least square values;
    All these keywords.

    JEL classification:

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

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