In such a type space, player 1 assigns probability 1 to player 2 playing l, and player 2 assigns probability 1 to player 1 playing u

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,