Coincidence Theorem and the Inner Core

Abstract

We prove a variant of Fan's coincidence theorem. Then, by applying it, we give another proof to a theorem on the nonemptiness of the inner core due to Aubin (1973) and Inoue (2011). Our coincidence theorem is a suitable mathematical tool for proving the nonemptiness of the inner core in the sense that one of the assumptions of our coincidence theorem is equivalent to the balancedness of a non-transferable utility (NTU) game when two correspondences are defined properly.