In this paper, we consider Nash implementability in general settings under the assumption that one may abstain. We show that in the case of at least two individuals, any social choice rule is Nash implementable by mechanisms with abstentions if and only if it is Nash implementable. Moreover, we introduce the notions of minimal participation and participation in equilibrium. We then study the possibility of Nash implementability by mechanisms that satisfy minimal participation or participation.

中文翻译：

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通过允许弃权的机制实现Nash

在本文中，我们在可能会弃权的假设下考虑一般环境中的Nash可实现性。我们表明，在至少两个人的情况下，任何社会选择规则只要且仅当纳什可实施时，才可以由具有弃权的机制实施。此外，我们介绍了最小参与和参与均衡的概念。然后，我们通过满足最少参与或最小参与的机制来研究Nash可实现性的可能性。