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Characterizations of the $$\textbf{u}$$ u -prenucleolus by dually- $$\textbf{u}$$ u -essential coalitions

Author

Listed:
  • Zsófia Dornai

    (HUN-REN Centre for Economic and Regional Studies, Institute of Economics
    Budapest University of Technology and Economics)

  • Miklós Pintér

    (Corvinus University of Budapest
    HUN-REN-BME-BCE Quantum Technology Research Group)

Abstract

We extend the theory of TU-games with utility functions, which is a generalization of TU-games with restricted cooperation, to include dual games. By using the theory of dual games, we define dually- $$\textbf{u}$$ u -essential coalitions and show that they characterize the $$\textbf{u}$$ u -prenucleolus of $$\textbf{u}$$ u -balanced games. Additionally, we demonstrate that the intersection of $$\textbf{u}$$ u -essential and dually- $$\textbf{u}$$ u -essential coalitions also forms a characterization set for the $$\textbf{u}$$ u -prenucleolus, provided that the $$\textbf{u}$$ u -least-core is a proper subset of the $$\textbf{u}$$ u -core.

Suggested Citation

  • Zsófia Dornai & Miklós Pintér, 2025. "Characterizations of the $$\textbf{u}$$ u -prenucleolus by dually- $$\textbf{u}$$ u -essential coalitions," Annals of Operations Research, Springer, vol. 349(3), pages 1575-1607, June.
    • Handle: RePEc:spr:annopr:v:349:y:2025:i:3:d:10.1007_s10479-025-06549-0
    DOI: 10.1007/s10479-025-06549-0
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