Inspired by Kajii (1992) and Askoura (2011, 2017), we introduce the notion of the weak $\alpha$-core for games with nonordered preferences and a continuum of agents. First, we extend the work of Kajii (1992) to games with spaces of strategies defined on Hausdorff topological vector spaces. Furthermore, we prove the nonemptiness of the weak $\alpha$-core. Finally, we establish the relations between normal-form games, games with nonordered preferences and games with pseudo-utilities.

中文翻译：

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弱者 $\alpha$无序偏好和智能体连续体的博弈的核心存在性定理

受Kajii（1992）和Askoura（2011，2017）的启发，我们介绍了弱者的概念。 $\alpha$-核心用于具有无序首选项和代理连续体的游戏。首先，我们将Kajii（1992）的工作扩展到具有在Hausdorff拓扑向量空间上定义的策略空间的游戏。此外，我们证明了弱者的非空性$\alpha$-核。最后，我们建立了正规形式的游戏，具有无序偏好的游戏和具有伪效用的游戏之间的关系。