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The Equal Surplus Division Value for Cooperative Games with a Level Structure

Abstract

In this paper, we investigate the equal surplus division value for cooperative games with a level structure, which is a sequence of coalition structures becoming coarser and coarser. We propose three axiomatizations of the value. Among them, the first two use different variations of the recent population solidarity axiom, and the third one invokes a special reduced game consistency axiom. Due to the existence of a level structure, our axioms impose special restrictions on the players we focus. We show that our value can be characterized with these axioms and other variations of well-known axioms, such as efficiency, standardness, and quotient game property. Besides characterizing the value, we also connect it to the recent field of ordered tree cooperative games, wherein we find that the iterative value can be viewed as a special case of our value.

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Notes

  1. 1.

    Note that van den Brink et al. (2016) focus on convex combinations of the equal division value and the ESD-value, thus axiomatizations of the two values are special cases of their axiomatizations. In this paper, for illustration, we just focus on the ESD-value.

  2. 2.

    van den Brink et al. (2016) use a different population solidarity proposed by Chun and Park (2012). Nonetheless, as indicated by Chun and Park (2012), “population fairness implies both population solidarity and population fair-ranking”. It is therefore the population solidarity in van den Brink et al. (2016) can be replaced with population fairness, which is stronger than our population solidarity.

  3. 3.

    Another kind of amalgamation game can be found in Albizuri et al. (2006). For relationships between the two amalgamation games, see Alonso-Meijide et al. (2012).

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Acknowledgements

This work was supported by the National Nature Science Foundation of China (71901076) and the National Social Science Fund of China (18ZDA043).

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Correspondence to Deng-Feng Li.

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Communicated by Edith van der Wal.

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Hu, XF., Li, DF. The Equal Surplus Division Value for Cooperative Games with a Level Structure. Group Decis Negot (2020). https://doi.org/10.1007/s10726-020-09680-4

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Keywords

  • Cooperative game
  • Level structure
  • Equal surplus division value
  • Axiomatization
  • Ordered tree cooperative game

Mathematics Subject Classification

  • 91A12
  • 91A43

JEL Classification

  • C71
  • D63