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

Zsófia Dornai () and Miklós Pintér ()
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Zsófia Dornai: HUN-REN Centre for Economic and Regional Studies, Institute of Economics
Miklós Pintér: Corvinus University of Budapest

Annals of Operations Research, 2025, vol. 349, issue 3, No 4, 1575-1607

Abstract: 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.

Keywords: TU-games; Restricted cooperation; Prenucleolus; Least-core; Characterization set; Dual game; Anti-prenucleolus; TU-games with utility functions (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-025-06549-0

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