Sufficient conditions for the existence of stable sets of cooperative games

Naoki Matsumoto () and Masaki Minegishi ()
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Naoki Matsumoto: Keio University
Masaki Minegishi: Seikei University

Economics Bulletin, 2020, vol. 40, issue 3, 1958-1962

Abstract: In 1944, von Neumann and Morgenstern introduced a stable set of $n$-person cooperative games in characteristic function form, with transferable utility (called TU-games for short), which is the first solution concept for cooperative games with at least three players. It is known that every $n$-person game has a stable set if $n in {3,4}$. On the other hand, Lucas constructed a 10-person TU-game which has no stable set. However, for $5 leq n leq 9$, it is not known whether every $n$-person TU-game has a stable set. In this paper, we show two sufficient conditions for an $n$-person TU-game to have a stable set for any $ngeq 5$.

Keywords: Cooperative game; TU-game, Stable set. (search for similar items in EconPapers)
JEL-codes: C7 (search for similar items in EconPapers)
Date: 2020-07-14
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