We show that a strategy profile of a normal form game is proper if and only if it is quasi-perfect in every extensive form (with that normal form). Thus, properness requires optimality along a sequence of supporting trembles, while sequentiality only requires optimality in the limit.

A strategy profile of a normal form game is proper if and only if it is quas-perfect in every extensive form (with that normal form). Thus, properness requires optimality along a sequency of supporting trembles, while sequentiality only requires optimality in the limit.