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<p>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 <i>sub-game order preservation axioms</i>, 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 TU-games. 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.</p>

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Sub-game order preservation and values for TU-games

  • 期刊论文

  • 发表日期：

    2026年7月31日

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  • David Lowing,
  • Satoshi Nakada,
  • Florian Navarro

摘要

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 TU-games. 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.