A distributed system model is studied, where individual agents engage in repeated play against each other and can change their strategies based upon previous play. Similar to Dorofeenko and Shorish (2005), it is shown how to model this environment in terms of continuous population densities (probabilities) of agent types. A complication arises because the population densities of different strategies depend upon each other not only through game payoffs, but also through the strategy distributions themselves. In spite of this, it is shown that when an agent imitates the strategy of his previous opponent and the rate of this imitation is high enough, the system of master equations which govern the dynamical evolution of agent populations can be reduced with high precision to one equation for the total population. In a sense, the dynamics of the full system can 'collapse' to the dynamics of the entire system taken as a whole, which describes the behavior of all types of agents. We explore the implications of this model, and present both analytical and simulation results
