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arXiv · 2511.05001

Characterizations of Proportional Division Value in TU-Games via Fixed-Population Consistency

Yukihiko Funaki·Yukio Koriyama·Satoshi Nakada·Yuki Tamura
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Abstract

We study the proportional division value in TU-games, which distributes the grand coalition worth in proportion to the players' stand-alone worths. Focusing on fixed-population consistency, we characterize the proportional division value through three types of axioms: axioms concerning transformations of the grand coalition worth, composition axioms, and nullified-game consistency. The first type captures how payoffs respond when the grand coalition worth changes. The composition axioms require that the outcome be the same whether a game is solved directly or through a two-step procedure based on a reference allocation and an associated adjustment of the game. Nullified-game consistency requires that, when some players' payoffs are fixed, the solution for the remaining players in the adjusted game coincides with their original payoffs. Together with efficiency and/or fairness-related conditions where appropriate, these axioms characterize the proportional division value.

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Yukihiko Funaki, Yukio Koriyama, Satoshi Nakada, Yuki Tamura. 2025-11-07. Characterizations of Proportional Division Value in TU-Games via Fixed-Population Consistency. https://arxiv.org/abs/2511.05001

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