In this paper, we propose three new axiomatizations of the Owen value, similar as the axiomatizations of the Shapley value of Chun (Int J Game Theory 20(2):183–190, 1991), van den Brink (Int J Game Theory 30(3):309–319, 2002), and Manuel et al. (Math Methods Oper Res 77:1–14, 2013), respectively. Firstly, we show that the additivity and null player property in Owen’s (in: Henn and Moeschlin (eds) Mathematical economics and game theory, Springer-Verlog, Berlin, 1977) axiomatization can be weakened into coalitional strategic equivalence. And then, we prove that the coalitional symmetry (respectively symmetry within union) and additivity in Owen’s (in: Henn and Moeschlin (eds) Mathematical economics and game theory, Springer-Verlog, Berlin, 1977) axiomatization can be weakened into a variation of fairness, named as coalitional fairness (respectively fairness within union). Finally, we show that the two fairness axioms in our second axiomatization can be weakened into two axioms, involving a special relation between players, named as indifference. Besides characterizing the Owen value, we also illustrate that our results can be extended to the Winter value, being a common single-valued solution for cooperative games with a level structure.

在本文中，我们提出了 Owen 值的三个新公理化，类似于 Chun (Int J Game Theory 20(2):183–190, 1991)、van den Brink (Int J Game Theory 30 (3):309–319, 2002) 和 Manuel 等人。(Math Methods Oper Res 77:1–14, 2013)，分别。首先，我们证明了欧文（在：Henn 和 Moeschlin (eds) 数学经济学和博弈论，Springer-Verlog，柏林，1977 年）公理化中的可加性和空玩家属性可以弱化为联盟战略等价。然后，我们证明了欧文 (Henn and Moeschlin (eds) Mathematicaleconomics and game theory, Springer-Verlog, Berlin, 1977) 中的联合对称性（分别为联合内的对称性）和可加性公理化可以弱化为公平，称为联盟公平（分别是联盟内的公平）。最后，我们证明了第二个公理化中的两个公平公理可以弱化为两个公理，涉及玩家之间的特殊关系，称为无差异。除了表征 Owen 值，我们还说明我们的结果可以扩展到 Winter 值，这是具有级别结构的合作游戏的常见单值解决方案。