Why Game Theory Assumes Everyone Is Rational (Common Knowledge)

Why this matters

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.

Demo

A fact $p$ is common knowledge among a group of players when everyone knows $p$, everyone knows that everyone knows $p$, and so on, all the way up. Formally, the shared-knowledge operator iterated:

Try it yourself

1. In the Prisoner's Dilemma, trace exactly which levels of knowledge are needed to predict defection. 'I'm rational' is one level; 'I know they're rational' is the second. How far do you need to go?
2. Find a real situation where you knew something and the other person knew it, but you didn't know they knew. How did the ambiguity shape the outcome?
3. The 'muddy children' puzzle is the classic illustration of common knowledge. Look it up and explain in one sentence why the father's public announcement changes the children's behavior, even though he told them nothing they didn't already know.
4. Generate one small example from your workplace where someone behaves 'irrationally' — and locate which level of common knowledge actually broke.

References

• Aumann — Agreeing to Disagree (Annals of Statistics, 1976)
• SEP — Common Knowledge