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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. Pongou, Roland & Tondji, Jean-Baptiste, 2024. "The reciprocity set," Journal of Mathematical Economics, Elsevier, vol. 112(C).

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