The $$\kappa $$ κ -core and the $$\kappa $$ κ -balancedness of TU games

David Bartl () and Miklós Pintér ()
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David Bartl: Silesian University in Opava
Miklós Pintér: Corvinus University of Budapest

Annals of Operations Research, 2024, vol. 332, issue 1, No 24, 689-703

Abstract: Abstract We consider transferable utility cooperative games with infinitely many players. In particular, we generalize the notions of core and balancedness, and also the Bondareva–Shapley Theorem for infinite TU games with and without restricted cooperation, to the cases where the core consists of $$\kappa $$ κ -additive set functions. Our generalized Bondareva–Shapley Theorem extends previous results by Bondareva (Problemy Kibernetiki 10:119–139, 1963), Shapley (Naval Res Logist Q 14:453–460, 1967), Schmeidler (On balanced games with infinitely many players, The Hebrew University, Jerusalem, 1967), Faigle (Zeitschrift für Oper Res 33(6):405–422, 1989), Kannai (J Math Anal Appl 27:227–240, 1969; The core and balancedness, handbook of game theory with economic applications, North-Holland, 1992), Pintér (Linear Algebra Appl 434(3):688–693, 2011) and Bartl and Pintér (Oper Res Lett 51(2):153–158, 2023).

Keywords: TU games with infinitely many players; Bondareva–Shapley Theorem; $$\kappa $$ κ -Core; $$\kappa $$ κ -Balancedness; $$\kappa $$ κ -Additive set function; Duality theorem for infinite LPs (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05713-8

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