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Characterizing the ELS values with fixed-population invariance axioms

Author

Listed:
  • Funaki, Yukihiko
  • Koriyama, Yukio
  • Nakada, Satoshi
  • Tamura, Yuki

Abstract

We study efficient, linear, and symmetric (ELS) values, a central family of allocation rules for cooperative games with transferable-utility (TU-games) that includes the Shapley value, the CIS value, and the ENSC value. We first show that every ELS value can be written as the Shapley value of a suitably transformed TU-game. We then introduce three types of invariance axioms for fixed player populations. The first type consists of composition axioms, and the second type is active-player consistency. Each of these two types yields a characterization of a subclass of the ELS values that contains the family of least-square values. Finally, the third type is nullified-game consistency: we define three such axioms, and each axiom yields a characterization of one of the Shapley, CIS, and ENSC values.

Suggested Citation

  • Funaki, Yukihiko & Koriyama, Yukio & Nakada, Satoshi & Tamura, Yuki, 2026. "Characterizing the ELS values with fixed-population invariance axioms," Journal of Mathematical Economics, Elsevier, vol. 125(C).
    • Handle: RePEc:eee:mateco:v:125:y:2026:i:c:s0304406826000583
    DOI: 10.1016/j.jmateco.2026.103270
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