Ellison (1993) examines the dynamic implications of learning in large population coordination games, focusing on the structure of the matching process that determines how players interact. He builds on the work of Kandori, Mailath, and Rob (1993), showing that a combination of experimentation and myopia leads players to coordinate on the risk dominant equilibrium. The paper analyzes the convergence rates of dynamic systems in large populations with uniform and local matching rules. In uniform matching, where players interact with the entire population, the convergence to the risk dominant equilibrium is very slow, and the long-run limit may not be relevant for short time horizons. In contrast, with local matching, where players interact with a small group of neighbors, the convergence is much faster, and the risk dominant equilibrium is more likely to be reached. The paper shows that the nature of interactions within a population significantly affects the dynamics of play. Local interactions allow evolutionary forces to determine the outcome, while uniform interactions are more influenced by historical factors. The paper also discusses the long-run behavior of the models, showing that the steady-state distribution is concentrated on the risk dominant equilibrium for both uniform and local matching rules. However, the rate at which the system converges to this equilibrium differs significantly between the two models. For uniform matching, the convergence is extremely slow, while for local matching, it is much faster. The paper provides theoretical results and numerical simulations to support these findings, showing that the convergence rates are crucial for determining the relevance of evolutionary forces in economic systems. The results suggest that in large populations with local interactions, evolutionary forces are more effective in determining the outcome, and predictions based on these forces are robust to population size.Ellison (1993) examines the dynamic implications of learning in large population coordination games, focusing on the structure of the matching process that determines how players interact. He builds on the work of Kandori, Mailath, and Rob (1993), showing that a combination of experimentation and myopia leads players to coordinate on the risk dominant equilibrium. The paper analyzes the convergence rates of dynamic systems in large populations with uniform and local matching rules. In uniform matching, where players interact with the entire population, the convergence to the risk dominant equilibrium is very slow, and the long-run limit may not be relevant for short time horizons. In contrast, with local matching, where players interact with a small group of neighbors, the convergence is much faster, and the risk dominant equilibrium is more likely to be reached. The paper shows that the nature of interactions within a population significantly affects the dynamics of play. Local interactions allow evolutionary forces to determine the outcome, while uniform interactions are more influenced by historical factors. The paper also discusses the long-run behavior of the models, showing that the steady-state distribution is concentrated on the risk dominant equilibrium for both uniform and local matching rules. However, the rate at which the system converges to this equilibrium differs significantly between the two models. For uniform matching, the convergence is extremely slow, while for local matching, it is much faster. The paper provides theoretical results and numerical simulations to support these findings, showing that the convergence rates are crucial for determining the relevance of evolutionary forces in economic systems. The results suggest that in large populations with local interactions, evolutionary forces are more effective in determining the outcome, and predictions based on these forces are robust to population size.