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

TL;DR

This paper extends the concepts of core and balancedness in infinite TU-games by generalizing to $$-additive set functions and broadens the Bondareva-Shapley Theorem to these cases, advancing the theoretical understanding of cooperative game stability.

Contribution

It introduces a generalization of the core and balancedness notions for infinite TU-games using $$-additive set functions, extending the Bondareva-Shapley Theorem.

Findings

Generalization of core and balancedness for infinite TU-games.

Extension of the Bondareva-Shapley Theorem to $$-additive set functions.

Broader theoretical framework for cooperative game stability in infinite settings.

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).