One of the many important contributions in David Schmeidler's distinguished career was the introduction of the nucleolus. This paper is an update on the nucleolus and its two related supersolutions, i.e., the kernel and the bargaining set.

We provide nonemptiness results of approximate interim cores with endogenous communication in large quasilinear economies, where every agent's informational size is small. We offer results for both replica and more general sequences of economies.