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Most work in evolutionary game theory analyzes a deterministic adjustment process on a continuum of agents. However, both the assumption of a continuum and that of no randomness are approximations, so it is important to study the behavior of adjustment processes on a large but finite population subject to small but persistent stochastic shocks. This paper characterizes the properties of the invariant distribution of birth-death processes in the double limit as the population becomes infinitely large and the perturbation vanishingly small.
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