Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies are well-defined, then spurious Nash equilibria cannot appear; if...

We demonstrate that iterated elimination of strictly dominated strategies is an order dependent procedure. We also prove that order does not matter if strategy spaces are compact and payoff functions continous. Examples show that this result is tight.