Partial differential equation modelling for stochastic fixed strategy distributed systems

Fixed strategy models, in which agents are endowed with a behavioral strategy as a primitive of the economy, are widely used in distributed systems where interaction is governed by local effects. We introduce a methodology for analyzing such models using partial differential equation systems. This method is developed in detail and applied to an extended economic example, the demographic prisoner's dilemma. We show using this methodology that both analytical and numerical results may be obtained for the long-run dynamics of the stochastic system. The method thus complements existing simulation techniques for analyzing the long-run behavior of stochastic fixed strategy distributed systems.