INOUE Tomoki
Department Undergraduate School , School of Political Science and Economics Position Senior Assistant Professor |
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Language | English |
Publication Date | 2021 |
Type | Academic Journal |
Peer Review | Peer reviewed |
Title | Coincidence theorem and the inner core |
Contribution Type | Sole-authored |
Journal | Pure and Applied Functional Analysis |
Publisher | Yokohama Publishers |
Volume, Issue, Page | 6(4),pp.761-775 |
Total page number | 15 |
Details | 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. |