The Nonemptiness of the Inner Core

28 Pages Posted: 5 Nov 2011 Last revised: 26 Aug 2019

See all articles by Tomoki Inoue

Tomoki Inoue

Meiji University - School of Political Science and Economics

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

Inoue, Tomoki, The Nonemptiness of the Inner Core (August 25, 2019). Available at SSRN: https://ssrn.com/abstract=1954304 or http://dx.doi.org/10.2139/ssrn.1954304

Tomoki Inoue (Contact Author)

Meiji University - School of Political Science and Economics ( email )

1-1 Kanda-Surugadai
Chiyoda-ku, Tokyo 101-8301
Japan

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