Abstract
In game-theoretic equilibrium, players' beliefs about choices by others are statistically correct. This mutual consistency assumption often predicts poorly in one-shot games. We develop an alternative cognitive hierarchy (CH) theory. In the CH model players who are not thinking strategically (0 steps) randomize. Players doing k steps of thinking predict accurately what lower-level players (steps 0 to k − 1) do, and best-respond given their beliefs. The model can explain why equilibration is so limited in some games (such as p-beauty contest), and surprisingly accurate in other games (such as business entry). The average number of thinking steps is about 1.5 across many games.
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