First of all, how can agents arrive at a context where rationality is commonly believed? The above results do not answer that question. This has been the subject of recent work in Dynamic Epistemic Logic (van Benthem 2003). In this literature, this question is answered by showing that the agents can eliminate all higher-order uncertainty regarding each others’ rationality, and thus ensure that no strategy is played that would not survive the iterated elimination procedure, by repeatedly and publicly “announcing” that they are not irrational. In other words, iterated public announcement of rationality makes the players’ expectations converge towards sufficient epistemic conditions to play iteratively non-dominated strategies. For more on this dynamic view on solution epistemic characterization see van Benthem (2003); Pacuit &amp; Roy (2011); van Benthem &amp; Gheerbrant (2010); and van Benthem, Pacuit, &amp; Roy (2011).