Marginalism, Egalitarianism and E ciency in Multi-Choice Games

David Lowing and Kevin Techer ()
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Kevin Techer: GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Multi-choice games; Multi-choice Shapley value; Multi-choice Equal division value; Multi-choice Egalitarian Shapley values Multi-choice games; Multi-choice Egalitarian Shapley values (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-dcm, nep-gth and nep-isf
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