TY - JOUR
T1 - Marginalism, egalitarianism and efficiency in multi-choice games
AU - Lowing, David
AU - Techer, Kevin
N1 - Funding Information:
We thank Stéphane Gonzalez, Justin Leroux and Philippe Solal for useful comments. We thank Encarnacion Algaba and the EURO21 organizing committee for letting us present this paper at the EURO21 conference. We are also grateful to an associate editor and two anonymous reviewers for their comments on our work. The authors want to thank GRDF (Gaz Réseau Distribution France) for their financial support through the ANRT (Association Nationale Recherche Technologie) doctoral program CIFRE (Conventions Industrielles de Formation par la REcherche).
Funding Information:
We thank Stéphane Gonzalez, Justin Leroux and Philippe Solal for useful comments. We thank Encarnacion Algaba and the EURO21 organizing committee for letting us present this paper at the EURO21 conference. We are also grateful to an associate editor and two anonymous reviewers for their comments on our work. The authors want to thank GRDF (Gaz Réseau Distribution France) for their financial support through the ANRT (Association Nationale Recherche Technologie) doctoral program CIFRE (Conventions Industrielles de Formation par la REcherche).
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/11
Y1 - 2022/11
N2 - 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.
AB - 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.
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U2 - 10.1007/s00355-022-01412-8
DO - 10.1007/s00355-022-01412-8
M3 - Article
AN - SCOPUS:85130213355
SN - 0176-1714
VL - 59
SP - 815
EP - 861
JO - Social Choice and Welfare
JF - Social Choice and Welfare
IS - 4
ER -