The Nonemptiness of the Inner Core
28 Pages Posted: 5 Nov 2011 Last revised: 26 Aug 2019
Date Written: August 25, 2019
Abstract
We prove that if a non-transferable utility (NTU) game is cardinally balanced and if, at every individually rational and efficient payoff vector, every non-zero normal vector to the set of payoff vectors feasible for the grand coalition is strictly positive, then the inner core is nonempty. The condition on normal vectors is satisfied if the set of payoff vectors feasible for the grand coalition is non-leveled. An NTU game generated by an exchange economy where every consumer has a continuous, concave, and strongly monotone utility function satisfies our sufficient condition. Our proof relies on Qin's theorem on the nonemptiness of the inner core.
Keywords: inner core, inhibitive set, cardinal balancedness, NTU game
JEL Classification: C62, C71
Suggested Citation: Suggested Citation