Continuous approximations of stochastic evolutionary game dynamics

Continuous approximations that are ordinary differential equations (ODEs) or stochastic differential equations (SDEs) are often used to study the properties of discrete stochastic processes. We show that different ways of taking the continuous limit of the same model may result in either an ODE or a SDE and study the manner in which each approximates the discrete model. We compare the asymptotic properties of the continuous equations with those of the discrete dynamics and show that they tend to provide a better approximation when a gi ratel amount of variance of the discrete model is preserved in the continuous limit. Journal of Economic Literature Classification numbers: C6, C7, D8. (C) 2000 Academic Press.