Finite memory distributed systems

A distributed system model is studied, where individual agents play repeatedly against each other and change their strategies based upon previous play. It is shown how to model this environment in terms of continuous population densities 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 at a sufficiently high rate, the system of equations which governs the dynamical evolution of agent populations can be reduced to one equation for the total population. In a sense, the dynamics '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.