Continuous approximations of stochastic evolutionary game dynamics (Q1841177)

The paper deals with a model of imitation, i.e. a discrete stochastic model which describes the change of the composition of different types in a given population. The change of the composition is caused by the imitation process [ cf. \textit{A.~Banerjee}, Q. J. Econ. 116, No. 1, 189--227 (2001; Zbl 0979.91021)]. The focus of the paper is on the construction of continuous limit for specific discrete imitation model. Under different assumptions, two limits of the same discrete model can be obtained: ordinary differential equations and stochastic differential equation. Asymptotic properties of the continuous and discrete models are compared.