Many authors have pointed out the strength of the common belief assumption in the results of the previous section (see, e.g., Gintis 2009; Bruin 2010). It requires that the players not only believe that the others are not choosing an irrational strategy, but also to believe that everybody believes that nobody is choosing an irrational strategy, and everyone believes that everyone believes that everyone believes that nobody is choosing an irrational strategy, and so on. It should be noted, however, that this unbounded character is there only to ensure that the result holds for arbitrary finite games. For a particular game and a model for it, a finite iteration of “everybody believes that” suffices to ensure a play that survives the iterative elimination procedure.