Trimmed equilibrium

Subgame perfect equilibrium (SPE) imposes stronger rationality conditions than necessary to ensure equilibrium outcomes are consistent with its concept. This is demonstrated by characterizing the maximal collection of information sets at which play is irrelevant for an outcome’s consistency with SPE. It is shown that, without affecting the set of equilibrium outcomes, equilibrium conditions can be trimmed by relaxing all conditions on this maximal collection. Therefore a trimmed SPE is a tight version of SPE. However, because its conditions are weaker, trimmed SPE might exist even if SPE does not. This is demonstrated in an application.