This paper explores the dynamic implications of learning in a large population coordination game, focusing on the structure of the matching process that describes how players interact. The author, Glenn Ellison, builds upon the work of Kandori, Mailath, and Rob (1993), who showed that a combination of experimentation and myopia can lead players to coordinate on the risk-dominant equilibrium. However, to assess the relevance of evolutionary forces, Ellison considers the rates at which dynamic systems converge to their long-run limits. Ellison introduces two extreme matching rules: uniform and local. In the uniform model, players are randomly matched, while in the local model, players interact with a small fixed subset of their peers. The paper analyzes the dynamics of these models, showing that in large populations with uniform matching, play is largely determined by historical factors. In contrast, local matching allows evolutionary forces to play a significant role, leading to rapid convergence to the risk-dominant equilibrium. The main theoretical results include: 1. **Steady State Distributions**: Both uniform and local models converge to a steady state where the risk-dominant equilibrium is played with high probability. 2. **Convergence Rates**: The rate of convergence is much faster in the local model compared to the uniform model, especially for small randomization probabilities. This means that in the local model, play can shift to the risk-dominant equilibrium within a few periods, while in the uniform model, it may take an extremely long time. The paper also discusses the robustness of these findings and their implications for understanding the development of conventions in large societies. The results suggest that local interaction can significantly influence the dynamics of coordination games, making evolutionary forces more relevant in practical economic systems.This paper explores the dynamic implications of learning in a large population coordination game, focusing on the structure of the matching process that describes how players interact. The author, Glenn Ellison, builds upon the work of Kandori, Mailath, and Rob (1993), who showed that a combination of experimentation and myopia can lead players to coordinate on the risk-dominant equilibrium. However, to assess the relevance of evolutionary forces, Ellison considers the rates at which dynamic systems converge to their long-run limits. Ellison introduces two extreme matching rules: uniform and local. In the uniform model, players are randomly matched, while in the local model, players interact with a small fixed subset of their peers. The paper analyzes the dynamics of these models, showing that in large populations with uniform matching, play is largely determined by historical factors. In contrast, local matching allows evolutionary forces to play a significant role, leading to rapid convergence to the risk-dominant equilibrium. The main theoretical results include: 1. **Steady State Distributions**: Both uniform and local models converge to a steady state where the risk-dominant equilibrium is played with high probability. 2. **Convergence Rates**: The rate of convergence is much faster in the local model compared to the uniform model, especially for small randomization probabilities. This means that in the local model, play can shift to the risk-dominant equilibrium within a few periods, while in the uniform model, it may take an extremely long time. The paper also discusses the robustness of these findings and their implications for understanding the development of conventions in large societies. The results suggest that local interaction can significantly influence the dynamics of coordination games, making evolutionary forces more relevant in practical economic systems.