In this paper, we investigate processes involving iterative information updating due to van Benthem (Int Game Theory Rev 9: 13—45, 2007), who characterized existent game-theoretic solution concepts by such processes in the framework of Plaza's public announcement logic. We refine this approach and clarify the relationship between stable strategies and information update processes. After extending Plaza's logic, we then derive the conditions under which a stable outcome is determined independently of the order of the iterative information updates. This result gives (...) an epistemic foundation for the order independence of iterated elimination of disadvantageous strategies. (shrink)