Abreu and Sen (J Econ Theory 50(2):285–299, 1990) provide a necessary condition, called Condition \(\alpha \), which is almost sufficient for a social choice rule to be implementable via subgame perfect equilibria. Yet, it is not straightforward to check the satisfaction of Condition \(\alpha \). We contribute in this direction by establishing a nuanced picture over the subgame perfect implementability of compromise rules, as a function of the compromise threshold. This contrasts with scoring rules that all fail to be subgame perfect implementable and with several Condorcet rules which are subgame perfect implementable.

Abreu和Sen（J Econ Theory 50（2）：285-299，1990）提供了一个必要条件，称为Condition \（\ alpha \），这几乎足以通过子博弈完美均衡实现社会选择规则。然而，要检查条件\（\ alpha \）的满足度并不是一件容易的事。我们通过在子游戏中根据折衷阈值完善折衷规则的完美可实现性，来为这一方向做出贡献。这与不能完全实现子游戏的计分规则和一些可以完美实现子游戏的Condorcet规则形成对比。