Sub-game order preservation and values for TU-games

David Lowing (), Satoshi Nakada and Florian Navarro
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David Lowing: ENS Rennes - École normale supérieure - Rennes, CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique
Satoshi Nakada: Tokyo University of Science

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Abstract: In cooperative games with transferable utility (TU-games), a player's contribution may vary depending on the coalition they join, reflecting different levels of synergy with other members. In this paper, we introduce a family of axioms referred to as sub-game order preservation axioms, which formalize the intuition that a player's payoff should increase with the degree of synergy they exhibit within a coalition. We propose four distinct axioms, each of which captures a different interpretation of what constitutes synergy in the context of transferable utility. We demonstrate that one of these variants is incompatible with the classical Efficiency axiom, thereby giving rise to an impossibility result. The remaining three axioms, when combined with Efficiency, lead to unique characterizations of three well-known solution concepts: the Shapley value, the Center of the Imputation Set (CIS), and the Equal Allocation of Non-Separable Contributions (ENSC) value, respectively.

Keywords: CIS value; ENSC value; TU-games; Sub-game order preservation; Shapley value (search for similar items in EconPapers)
Date: 2026
Note: View the original document on HAL open archive server: https://hal.science/hal-05153554v2
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Published in International Journal of Game Theory, In press

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Working Paper: Sub-game order preservation and values for TU-games (2025)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05153554

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