Abstract
We consider multi-choice cooperative games with a permission tree structure. Multi-choice games are a generalization of cooperative transferable utility games in which each player has several activity levels. In addition, a permission tree structure models a situation in which a player needs permission from another player to cooperate. In this framework, the influence of a permission structure on the possibility of cooperation may have several interpretations depending on the context. In this paper, we investigate several of these interpretations and introduce for each of them a new allocation rule that we axiomatically characterize.
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Notes
We continue to denote the sovereign part and the authorizing part of s by \(\sigma (s)\) and \(\alpha (s)\) with the understanding that the underlying permission structure is \(S^+_m\).
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Acknowledgements
We are grateful to an anonymous reviewer for their comments on our work. We also thank Sylvain Béal, Stéphane Gonzalez, Kevin Techer and Philippe Solal for useful comments. We are grateful to Encarnación Algaba and the EURO21 organizing committee for letting us present this paper at the EURO21 conference, Eric Bahel for letting us present this paper at the International Conference on Social Choice and Voting Theory, and the SING16 organizing committee for letting us present this paper at the European Meeting on Game Theory (2021). The author wants 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).
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Lowing, D. Allocation rules for multi-choice games with a permission tree structure. Ann Oper Res 320, 261–291 (2023). https://doi.org/10.1007/s10479-022-04953-4
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DOI: https://doi.org/10.1007/s10479-022-04953-4