イノウエ　トモキ   INOUE Tomoki   井上　朋紀    所属   明治大学  政治経済学部    職種   専任講師
言語種別	英語
発行・発表の年月	2021
形態種別	学術雑誌
査読	査読あり
標題	Coincidence theorem and the inner core
執筆形態	単著
掲載誌名	Pure and Applied Functional Analysis
出版社・発行元	Yokohama Publishers
巻・号・頁	6(4),pp.761-775
総ページ数	15
概要	We provide two coincidence theorems that are useful mathematical tools for proving the nonemptiness of the inner core. The inner core is a refinement of the core of non-transferable utility (NTU) games. Our first coincidence theorem is a synthesis of Brouwer's fixed point theorem and Debreu and Schmeidler's separation theorem for convex sets. Our second coincidence theorem is a modification of the first one in order for two correspondences to have a nonempty intersection at a strictly positive vector. Inoue's theorem on the nonemptiness of the inner core follows from our first coincidence theorem and an assumption on the efficient surface of payoff vectors for the grand coalition. Our coincidence theorems are suitable for proving the nonemptiness of the inner core in the sense that one of the assumptions in our first coincidence theorem is equivalence to the cardinal balancedness of an NTU game when two correspondences are defined properly.