Efficiency and the core in NTU games in partition function form

The aim of this paper is to establish a necessary and sufficient condition for the non-emptiness of the core in NTU games in partition function form, given an externality scheme \( f \in \textsf{Ex}(N) \) $f\in \mathsf{Ex}(N)$ . We extend the notion of convexity to incorporate externality effects. By introducing a new concept of rationality, called collective rationality, we demonstrate the efficiency of the grand coalition \( N \) $N$ . We also identify a sufficient condition for the efficiency of the grand coalition using the property of individual superadditivity.