论文标题
在无限很多玩家的平衡游戏中：重新访问施密特勒的结果
On Balanced Games with Infinitely Many Players: Revisiting Schmeidler's Result
论文作者
论文摘要
我们考虑具有无限很多玩家的可转让公用事业合作游戏，并且在有限的加法设置功能的空间中理解了核心。我们表明，如果游戏在下面有限，那么仅当游戏保持平衡时，其核心是非空的。 这一发现是对Schmeidler（1967）的原始结果的概括``在无限很多玩家的平衡游戏中''，其中该游戏被认为是非负的。此外，我们证明，如果游戏不在下面，那么即使游戏平衡，它的核心也可能是空的。也就是说，我们的结果很紧。 我们还将Schmeidler（1967）的结果推广到限制合作的情况下。
We consider transferable utility cooperative games with infinitely many players and the core understood in the space of bounded additive set functions. We show that, if a game is bounded below, then its core is non-empty if and only if the game is balanced. This finding is a generalization of Schmeidler's (1967) original result ``On Balanced Games with Infinitely Many Players'', where the game is assumed to be non-negative. We furthermore demonstrate that, if a game is not bounded below, then its core might be empty even though the game is balanced; that is, our result is tight. We also generalize Schmeidler's (1967) result to the case of restricted cooperation too.
