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| Naoki Matsumoto and Masaki Minegishi |
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| ''Sufficient conditions for the existence of stable sets of cooperative games'' |
| ( 2020, Vol. 40 No.3 ) |
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| 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 $ngeq 5$. |
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| Keywords: Cooperative game; TU-game, Stable set. |
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| Manuscript Received : May 04 2020 | | Manuscript Accepted : Jul 14 2020 |
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