 Strong rationality is a more demanding condition than weak rationality. While SR implies WR, there can be moves that satisfy weak but not strong rationality. This shows in the following difference between the current and the previous example. In the present matrix, announcing Weak Rationality stops after the first step elimination of action c. The reason is that, in the second matrix, the row player’s bottom move is not strictly dominated by any other action, so this row remains after re-announcing WR. However, under no possible circumstance is the row player’s bottom action best for her. This contradicts strong rationality and hence that row is eliminated by the next SR announcement. More generally, the game matrix resulting from \((\textit{SR})^\infty\) is a sub-matrix of that produced by \((\textit{WR})^\infty\). Notably, this is not entirely obvious, as the two update sequences may produce different epistemic models satisfying different formulas. A proof can be found in van Benthem (2014).