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Estate Division Problem: The Core and The Godly Interference

Author

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  • Anirban Ghatak

    (Indian Institute of Management Kozhikode)

Abstract

This article offers a simple method to reduce the Core of a Transferable Utility game to a singleton where the Core happens to have more than one elements in it. By presenting a popular folklore, this article infers that the solution of an integer-constrained estate division problem can be achieved by introducing a temporary player who gets no utility by participating in the game. This article refers to this temporary player as a god. It shows that such god -ly interference can help us to make sense the Core by making it a unique one.

Suggested Citation

  • Anirban Ghatak, 2022. "Estate Division Problem: The Core and The Godly Interference," Working papers 497, Indian Institute of Management Kozhikode.
    • Handle: RePEc:iik:wpaper:497
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    References listed on IDEAS

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    1. Vito Fragnelli & Stefano Gagliardo & Fabio Gastaldi, 2014. "Integer solutions to bankruptcy problems with non-integer claims," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 892-933, October.
    2. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    3. Vito Fragnelli & Fabio Gastaldi, 2017. "Remarks on the integer Talmud solution for integer bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 127-163, April.
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