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Abstract <p> We analyze connections between the Shapley value and the core of the well-known Aubinextension of an almost positive cooperative game. Nonnegative Harsanyi dividends characterizesuch games up to an additive component. Since each almost positive game is convex, its corecontain the Shapley value. We prove a stronger connection for the Aubin extension of sucha game; namely, the core is a singleton consisting of the corresponding Shapley value. Aubinmentioned that, for certain classes of fuzzy cooperative games, it is possible to describe the core interms of the superdifferential of the characteristic function. Our arguments are based on this fact.</p>

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On the Core of the Aubin Extension of an Almost Positive Game

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • V. A. Vasil’ev

摘要

Abstract

We analyze connections between the Shapley value and the core of the well-known Aubinextension of an almost positive cooperative game. Nonnegative Harsanyi dividends characterizesuch games up to an additive component. Since each almost positive game is convex, its corecontain the Shapley value. We prove a stronger connection for the Aubin extension of sucha game; namely, the core is a singleton consisting of the corresponding Shapley value. Aubinmentioned that, for certain classes of fuzzy cooperative games, it is possible to describe the core interms of the superdifferential of the characteristic function. Our arguments are based on this fact.