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Game theory's predictions quietly rest on assumptions like 'both players are rational' and 'both players know the other is rational' — ad infinitum. That chain is called common knowledge of rationality, and when it breaks, predictions break with it. The real world has children, drunk drivers, stressed-out executives, and software bugs — all of whom violate common knowledge somewhere. Understanding exactly which step of the chain a situation breaks is how you know whether to apply game theory or psychology.
A fact is common knowledge among a group of players when everyone knows , everyone knows that everyone knows , and so on, all the way up. Formally, the shared-knowledge operator iterated:
Use these three in order. Each builds on the one before.
Explain 'common knowledge' in plain terms and why it's stronger than just 'everyone knows it'.
Walk me through the muddy children puzzle step by step — how does the public announcement actually add new information even though every child already knew some children were muddy?
In finance, a famous paper (Milgrom & Stokey) argues rational traders with common knowledge can't agree to speculative trades. Intuitively, why? Where does real-market behavior break the assumption?