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Marginalism, Egalitarianism and E ciency in Multi-Choice Games

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Abstract

The search for a compromise between marginalism and egalitarianism has given rise to many discussions. In the context of cooperative games, this compromise can be understood as a trade-off between the Shapley value and the Equal division value. We investigate this compromise in the context of multi-choice games in which players have several activity levels. To do so, we propose new extensions of the Shapley value and of the Weighted Division values to multi-choice games. Contrary to the existing solution concepts for multi-choice games, each one of these values satisfies a core condition introduced by Grabisch and Xie (2007), namely Multi-Efficiency. We compromise between marginalism and egalitarianism by introducing the multi-choice Egalitarian Shapley values, computed as the convex combination of our extensions. To conduct this study, we introduce new axioms for multi-choice games. This allows us to provide an axiomatic foundation for each of these values.
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halshs-03334056 , version 1 (03-09-2021)

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  • HAL Id : halshs-03334056 , version 1

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David Lowing, Kevin Techer. Marginalism, Egalitarianism and E ciency in Multi-Choice Games. 2021. ⟨halshs-03334056⟩
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