We introduce extended proper equilibrium, which refines proper equilibrium (Myerson, 1978) by adding across-player restrictions on trembles. This refinement coincides with proper equilibrium in games with two players but adds new restrictions in games with three or more players. One implication of these additional restrictions is that any tremble that is costless in equilibrium is regarded by all as more likely than any costly tremble, even one by a different player. At least one extended proper equilibrium exists in every finite game. The refinement can also be characterized in terms of a symmetric, meta-version of the game in which players originate from a common pool: if these players tremble symmetrically and in the way of proper equilibrium, then the induced play in the original game is an extended proper equilibrium.

我们引入扩展的适当平衡，通过在战友身上增加对战栗的限制来完善适当的平衡（Myerson，1978年）。这种改进与具有两个玩家的游戏中的适当平衡相吻合，但为具有三个或更多玩家的游戏增加了新的限制。这些附加限制的一个含义是，在均衡中无代价的任何颤抖都比任何代价高昂的颤抖更有可能被视为所有人，即使是另一位参与者也是如此。每个有限博弈中至少存在一个扩展的适当均衡。改进还可以根据游戏的对称元版本来描述，其中玩家来自一个共同的池：如果这些玩家对称地颤抖并且以适当的平衡方式颤抖，那么原始游戏中的诱导游戏就是扩展了适当的平衡。