The paper introduces a cognitive hierarchy (CH) model of games as an alternative to equilibrium theory. In equilibrium theory, players are assumed to be rational and accurately predict others' strategies, but in many experiments, players are not in equilibrium. The CH model assumes that each player believes they understand the game better than others, and that their strategies are based on the assumption that others are distributed across different levels of strategic thinking. The model inductively defines strategic categories: step 0 players randomize; step k players best-respond, assuming others are distributed across steps 0 through k-1. The CH model fits empirical data and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games. The CH model is based on a Poisson distribution of thinking steps, with a parameter τ that determines the average number of steps. The model explains why the convergence process stops at an average around 30 in the beauty contest game, rather than converging to the equilibrium of zero. It also explains the "instant equilibration" in business entry games. Values of τ between 1 and 2 explain empirical results for nearly 100 games, suggesting that assuming a τ value of 1.5 could give reliable predictions for many other games. The paper discusses the theoretical properties of the Poisson-CH model, including its ability to explain dominance-solvable games, coordination games, and market entry games. The model is compared to Nash equilibrium in several games, and it is shown that the Poisson-CH model fits the data better in many cases. The model is also shown to have economic value, as it can predict behavior more accurately than Nash equilibrium in many situations. The paper concludes that the Poisson-CH model provides a useful framework for understanding strategic behavior in games, and that it has potential applications in economics and other fields.The paper introduces a cognitive hierarchy (CH) model of games as an alternative to equilibrium theory. In equilibrium theory, players are assumed to be rational and accurately predict others' strategies, but in many experiments, players are not in equilibrium. The CH model assumes that each player believes they understand the game better than others, and that their strategies are based on the assumption that others are distributed across different levels of strategic thinking. The model inductively defines strategic categories: step 0 players randomize; step k players best-respond, assuming others are distributed across steps 0 through k-1. The CH model fits empirical data and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games. The CH model is based on a Poisson distribution of thinking steps, with a parameter τ that determines the average number of steps. The model explains why the convergence process stops at an average around 30 in the beauty contest game, rather than converging to the equilibrium of zero. It also explains the "instant equilibration" in business entry games. Values of τ between 1 and 2 explain empirical results for nearly 100 games, suggesting that assuming a τ value of 1.5 could give reliable predictions for many other games. The paper discusses the theoretical properties of the Poisson-CH model, including its ability to explain dominance-solvable games, coordination games, and market entry games. The model is compared to Nash equilibrium in several games, and it is shown that the Poisson-CH model fits the data better in many cases. The model is also shown to have economic value, as it can predict behavior more accurately than Nash equilibrium in many situations. The paper concludes that the Poisson-CH model provides a useful framework for understanding strategic behavior in games, and that it has potential applications in economics and other fields.