Rational players should defect immediately. But cooperation pays MORE.
The Setup (Rosenthal, 1981): Two players alternate turns. Each turn, you can TAKE the pot (ending the game) or PASS (doubling the pot for the other player). The pot grows: 2→4→8→16→32→64... If you pass at round N, you get the "loser's share" if your opponent takes next.
The Paradox: Backward induction proves that rational players should TAKE immediately. But experiments show humans cooperate—and earn FAR more as a result!
Why "rational" players should defect at round 1:
| Strategy | Player 1 Gets | Player 2 Gets | Total |
|---|---|---|---|
| Rational (Take at Round 1) | $1 | $0 | $1 |
| Full Cooperation (6 rounds) | $32 | $64 | $96 |
The "rational" outcome is 96x worse than cooperation!
In lab experiments, humans typically cooperate until rounds 4-5, earning much more than backward induction predicts. Only 2-3% defect at round 1 as "rationality" demands.
Most humans reason 2-3 steps ahead, not infinitely. A "Level-2" player thinks: "My opponent might cooperate, so I should pass for now." This bounded rationality pays off!
Backward induction requires COMMON KNOWLEDGE of rationality—everyone knows everyone knows everyone is rational... ad infinitum. This rarely holds in practice.
In repeated games, cooperation builds trust. Even in one-shot games, humans import social norms. "Irrational" cooperation may be evolutionarily adaptive.