Note that, the above process need not generate all strategies that survive iteratively removing strictly dominated strategies. For example, consider a type space with a single type for player 1 assigning probability 1 to the single type of player 2 and \(l\), and the single type for player 2 assigning probability 1 to the single type for player 1 and \(u\). Then, \((u,l)\) is the only strategy profile in this model and obviously rationality and common belief of rationality is satisfied. However, for any type space, if a strategy profile is consistent with rationality and common belief of rationality, then it must be a strategy that is in the set of strategies that survive iteratively removing strictly dominated strategies.