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Characterizing the ELS Values with Fixed-Population Invariance Axioms

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  • Yukihiko Funaki
  • Yukio Koriyama
  • Satoshi Nakada
  • Yuki Tamura

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

  • Yukihiko Funaki & Yukio Koriyama & Satoshi Nakada & Yuki Tamura, 2025. "Characterizing the ELS Values with Fixed-Population Invariance Axioms," Papers 2511.04996, arXiv.org.
    • Handle: RePEc:arx:papers:2511.04996
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    1. Ruiz, Luis M & Valenciano, Federico & Zarzuelo, Jose M, 1996. "The Least Square Prenucleolus and the Least Square Nucleolus. Two Values for TU Games Based on the Excess Vector," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 113-134.
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