Continuous approximations of stochastic evolutionary game dynamics

Continuous approximations that are ordinary differential equations (ODEs) o r stochastic differential equations (SDEs) are often used to study the prop erties of discrete stochastic processes. We show that different ways of tak ing 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 o f the discrete dynamics and show that they tend to provide a better approxi mation when a gi ratel amount of variance of the discrete model is preserve d in the continuous limit. Journal of Economic Literature Classification nu mbers: C6, C7, D8. (C) 2000 Academic Press.