The paper introduces the Cognitive Hierarchy (CH) model, an alternative to equilibrium theory that explains empirical behavior in games. In CH, players assume their strategy is the most sophisticated, and the model defines strategic categories: step 0 players randomize, and step $k$ thinkers best-respond, assuming other players are distributed over steps 0 through $k-1$. The model fits empirical data and explains why equilibrium theory predicts behavior well in some games but poorly in others. On average, 1.5 steps fit data from many games. The CH model consists of iterative decision rules for players doing $k$ steps of thinking, with a frequency distribution $f(k)$ (assumed Poisson) of step $k$ players. The iteration begins with "step 0" types who randomize and moves to higher steps, where players accurately predict the relative frequencies of lower steps but ignore the possibility of higher steps. The Poisson distribution is characterized by a single parameter $\tau$, which is the mean and variance. A median estimate of $\hat{\tau}=1.61$ explains why the convergence process stops at an average around 30 in the beauty contest game, rather than converging to the equilibrium of zero. The paper discusses the theoretical properties of the Poisson-CH model, including its ability to link thinking steps to iterated deletion of dominated strategies and its predictions in coordination games and market entry games. It also compares the model's fit to Nash equilibrium across various games and models, showing that the Poisson-CH model fits data better than Nash in most cases. The model's predictions are generally more accurate in mixed games than in matrix games. Finally, the paper explores the economic value of theories, measuring how much greater payoffs players earn when they best-respond to a theory's forecast compared to responding naively.The paper introduces the Cognitive Hierarchy (CH) model, an alternative to equilibrium theory that explains empirical behavior in games. In CH, players assume their strategy is the most sophisticated, and the model defines strategic categories: step 0 players randomize, and step $k$ thinkers best-respond, assuming other players are distributed over steps 0 through $k-1$. The model fits empirical data and explains why equilibrium theory predicts behavior well in some games but poorly in others. On average, 1.5 steps fit data from many games. The CH model consists of iterative decision rules for players doing $k$ steps of thinking, with a frequency distribution $f(k)$ (assumed Poisson) of step $k$ players. The iteration begins with "step 0" types who randomize and moves to higher steps, where players accurately predict the relative frequencies of lower steps but ignore the possibility of higher steps. The Poisson distribution is characterized by a single parameter $\tau$, which is the mean and variance. A median estimate of $\hat{\tau}=1.61$ explains why the convergence process stops at an average around 30 in the beauty contest game, rather than converging to the equilibrium of zero. The paper discusses the theoretical properties of the Poisson-CH model, including its ability to link thinking steps to iterated deletion of dominated strategies and its predictions in coordination games and market entry games. It also compares the model's fit to Nash equilibrium across various games and models, showing that the Poisson-CH model fits data better than Nash in most cases. The model's predictions are generally more accurate in mixed games than in matrix games. Finally, the paper explores the economic value of theories, measuring how much greater payoffs players earn when they best-respond to a theory's forecast compared to responding naively.