When lexicographically undominated strategies yield perfect equilibria

Perfect equilibrium, in which players share a common idea about future errors, is a widely used equilibrium concept for finite extensive-form games. Okada's (1991) lexicographic domination, by contrast, is based on each player's individual idea about future errors. We identify simple sufficient conditions under which perfect equilibria and lexicographically undominated strategy profiles are equivalent. For example, if each path includes at most two decision nodes, any lexicographically undominated strategy profile is perfect. When we consider a simple signaling game where the marginal impact of the receiver's action on the sender's payoff is type-invariant, if the receiver can select a special action called the Never-Best boundary action, both concepts coincide. Our results suggest that, under certain conditions, Selten's perfect equilibrium is consistent with weaker rationality assumptions than those underlying Selten's (1975) original definition.