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

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  • David Bartl
  • Mikl'os Pint'er

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 $\kappa$-additive set functions. Our generalized Bondareva-Shapley Theorem extends previous results by Bondareva (1963), Shapley (1967), Schmeidler (1967), Faigle (1989), Kannai (1969), Kannai (1992), Pinter(2011) and Bartl and Pint\'er (2022).

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  • David Bartl & Mikl'os Pint'er, 2022. "The $\kappa$-core and the $\kappa$-balancedness of TU games," Papers 2211.05843, arXiv.org.
    • Handle: RePEc:arx:papers:2211.05843
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    File URL: http://arxiv.org/pdf/2211.05843
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