Marginalism, egalitarianism and efficiency in multi-choice games

David Lowing and Kevin Techer ()
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Kevin Techer: Univ Lyon, UJM Saint-Etienne, GATE UMR 5824

Social Choice and Welfare, 2022, vol. 59, issue 4, No 2, 815-861

Abstract: 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 Equal division value 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 (Math Methods Oper Res 66(3):491–512, 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.

Date: 2022
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Working Paper: Marginalism, egalitarianism and efficiency in multi-choice games (2022)
Working Paper: Marginalism, Egalitarianism and Efficiency in Multi-Choice Games (2021)
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DOI: 10.1007/s00355-022-01412-8

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