Limit behavior Rationality is ‘self-fulfilling’ in the limit: if players commit to it in deliberation for long enough, they prune away all irrational moves and, a fortiori, all moves incompatible with common belief of rationality. The final outcome is a model with rational play at every point, a form of common knowledge of rationality. However, iterated announcements can also yield a different type of limit behavior: self-refutation. A prime example for this is the classic Muddy Children puzzle