The Nash axiom is a basic property of consistency in choice. This paper proposes weaker versions of the axiom and examines their logical implications. In particular, we demonstrate that weak Nash axioms are useful to understand the relationship between the Nash axiom and the path independence axiom. We provide an application of weak Nash axioms to the no-envy approach. We present a possibility result and an impossibility result.

中文翻译：

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选择函数和弱纳什公理

纳什公理是选择一致性的基本属性。本文提出了较弱版本的公理，并研究了它们的逻辑含义。特别是，我们证明了弱Nash公理对于理解Nash公理和路径独立公理之间的关系很有用。我们将弱纳什公理应用于无羡慕方法。提出可能性结果和不可能结果。