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The recursive nucleolus for partition function form games

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  • Yang, Guangjing
  • Sun, Hao

Abstract

To solve the problems about the emptiness and nonexistence of the recursive core (r-core) as introduced by Huang and Sjöström (2003), this paper considers a new recursive solution concept for partition function form games: the recursive nucleolus (r-nucleolus). In each recursive step, the prediction of a coalition about the partition of outsiders is consistent with the nucleolus in characteristic function form games. We show that the r-nucleolus is always nonempty, and it is a singleton in fully cohesive partition function form games. A sufficient condition is then provided to show that the r-nucleolus is included in the r-core. Additionally, some desirable properties that the r-nucleolus satisfies are presented. Moreover, we discuss applications of the r-nucleolus in Cournot oligopoly and Bertrand competition.

Suggested Citation

  • Yang, Guangjing & Sun, Hao, 2023. "The recursive nucleolus for partition function form games," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    • Handle: RePEc:eee:mateco:v:104:y:2023:i:c:s0304406822001173
    DOI: 10.1016/j.jmateco.2022.102791
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    1. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    2. Huang, Chen-Ying & Sjostrom, Tomas, 2006. "Implementation of the recursive core for partition function form games," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 771-793, September.
    3. Takaaki Abe & Yukihiko Funaki, 2021. "The projective core of symmetric games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 167-183, March.
    4. Bloch, Francis & van den Nouweland, Anne, 2014. "Expectation formation rules and the core of partition function games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 339-353.
    5. R. M. Thrall & W. F. Lucas, 1963. "N‐person games in partition function form," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 281-298, March.
    6. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Yang, Guangjing & Sun, Hao & Hou, Dongshuang & Xu, Genjiu, 2019. "Games in sequencing situations with externalities," European Journal of Operational Research, Elsevier, vol. 278(2), pages 699-708.
    8. Takaaki Abe & Yukihiko Funaki, 2017. "The non-emptiness of the core of a partition function form game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 715-736, August.
    9. Huang, Chen-Ying & Sjostrom, Tomas, 2003. "Consistent solutions for cooperative games with externalities," Games and Economic Behavior, Elsevier, vol. 43(2), pages 196-213, May.
    10. Parkash Chander, 2020. "Stability of the merger-to-monopoly and a core concept for partition function games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 953-973, December.
    11. Chen-Ying Huang & Tomas Sjöström, 2010. "The Recursive Core for Non-Superadditive Games," Games, MDPI, vol. 1(2), pages 1-23, April.
    12. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    13. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 157-171.
    14. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
    15. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
    16. Raymond Deneckere & Carl Davidson, 1985. "Incentives to Form Coalitions with Bertrand Competition," RAND Journal of Economics, The RAND Corporation, vol. 16(4), pages 473-486, Winter.
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    1. Pongou, Roland & Tondji, Jean-Baptiste, 2024. "The reciprocity set," Journal of Mathematical Economics, Elsevier, vol. 112(C).

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