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Sub-game order preservation and values for TU-games

Author

Listed:
  • David Lowing

    (CentraleSupélec, LGI - Laboratoire Génie Industriel - CentraleSupélec - Université Paris-Saclay)

  • Satoshi Nakada

    (Tokyo University of Science [Tokyo])

  • Florian Navarro

    (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

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.

Suggested Citation

  • David Lowing & Satoshi Nakada & Florian Navarro, 2025. "Sub-game order preservation and values for TU-games," Working Papers hal-05153554, HAL.
    • Handle: RePEc:hal:wpaper:hal-05153554
    Note: View the original document on HAL open archive server: https://hal.science/hal-05153554v1
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