On forward induction and evolutionary and strategic stability

We analyze which normal form solution concepts capture the notion of forward induction, as defined by van Damme (JET, 1989) in the class of generic two player normal form games preceded by an outside option. We find that none of the known strategic stability concepts (including Mertens stable sets and hyperstable sets) captures this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (Swinkels, JET, 1992) is always consistent with forward induction.