On the generic robustness of solution concepts to incomplete information

We consider the generic robustness of an upper hemi-continuous solution concept on a class of games of interest which has been embedded in a larger space of games. We show that generic robustness follows if the class of games of interest is “large” relative to the class of games in which it has been embedded. This result is used to show why interim correlated rationalizable actions are generically robust to players' hierarchies of beliefs as established by Weinstein and Yildiz (2007) even without their richness condition. It is also used to provide a formal sense according to which, in the setting of Kajii and Morris (1997b), the set of representations of a complete information game is small in the space of incomplete information games in which it is embedded. This difference in relative sizes makes the robustness problems of Kajii and Morris (1997b) and Weinstein and Yildiz (2007) be incomparable and helps explaining why their conclusions differ so significantly.