Marginalism, Egalitarianism and Efficiency in Multi-Choice Games

David Lowing and Kevin Techer (kevin.techer@univ-st-etienne.fr)
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Kevin Techer: Univ Lyon, UJM Saint-Etienne, GATE UMR 5824, F-42023 Saint- Etienne, France

No 2115, Working Papers from Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon

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 (search for similar items in EconPapers)
JEL-codes: C71 (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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Related works:
Journal Article: Marginalism, egalitarianism and efficiency in multi-choice games (2022)
Working Paper: Marginalism, egalitarianism and efficiency in multi-choice games (2022)
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