Continuous Approximations of Stochastic Evolutionary Game Dynamics

Valentina Corradi and Rajiv Sarin

ELSE working papers from ESRC Centre on Economics Learning and Social Evolution

Abstract: We derive continuous approximations of stochastic evolutionary dynamics in games. Depending on how we construct the continuous limit, we obtain a continuous approxi-mation that is either an ordinary differential equation (ODE) or a stochastic differential equation (SDE). Our SDE approximation result provides the first derivation of a SDE from an underlying discrete stochastic evolutionary game model. In deriving both an ODE and a SDE limit from the same model, our results provide information regarding the conditions under which the different limits arise.

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