Efficiency and the core in NTU games in partition function form

Abstract 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 $$ f \in \textsf{Ex}(N) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Ex</mml:mi> <mml:mo>(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . 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 $$ N $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> . We also identify a sufficient condition for the efficiency of the grand coalition using the property of individual superadditivity.