Sign properties and axiomatizations of the weighted division values

Wenzhong Li; Genjiu Xu; René van den Brink

doi:10.1016/j.jmateco.2024.102969

Sign properties and axiomatizations of the weighted division values

Wenzhong Li
, Genjiu Xu^*
, René van den Brink

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

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Abstract

In this paper, we study axiomatic foundations of the class of weighted division values. Firstly, while keeping efficiency, additivity and the nullifying player property from the original axiomatization of the equal division value, we consider relaxations of symmetry in line with Casajus (2019) to characterize the class of (positively) weighted division values. Secondly, we show that the class of weighted division values can also be characterized by replacing linearity in three axiomatizations of Béal et al. (2016) with additivity. Finally, we show how strengthening an axiom regarding null, non-negative, respectively nullified players in these three axiomatizations, provides three axiomatizations of the class of positively weighted division values.

Original language	English
Article number	102969
Pages (from-to)	1-7
Number of pages	7
Journal	Journal of Mathematical Economics
Volume	112
Early online date	16 Mar 2024
DOIs	https://doi.org/10.1016/j.jmateco.2024.102969
Publication status	Published - Jun 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.

Funding

The authors thank an editor and three anonymous referees for very helpful comments and suggestions. This work is supported by the National Natural Science Foundation of China (Grant Nos. 72301214 and 72071159 ), National Key R&D Program of China (Grant No. 2021YFA1000402 ) and Fundamental Research Funds for the Central Universities (Grant Nos. D5000230178 ).

Funders	Funder number
National Natural Science Foundation of China	72301214, 72071159
National Key Research and Development Program of China	2021YFA1000402
Fundamental Research Funds for the Central Universities	D5000230178

Keywords

Axiomatization
Cooperative game
Sign properties
Weighted division values

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10.1016/j.jmateco.2024.102969

Sign properties and axiomatizations of the weighted division valuesFinal published version, 587 KBLicence: Article 25fa Dutch Copyright Act

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KW - Cooperative game

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Sign properties and axiomatizations of the weighted division values

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