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Refinement of dynamic equilibrium using small random perturbations

. We propose a reﬁnement process of dynamic equilibria based on small random perturbations (SRP) of the backward perfect foresight (bpf) equilibrium map in a class of one-step forward looking dynamic models. An equilibrium is selected if its stationary measure is the limit of the stationary measures associated with the processes generated by the SRP of the bpf maps, as the perturbation size approaches zero. We show that, for full measure sets of parameter values of a large class of one-parameter families of unimodal bpf maps, only determinate cycles or the chaotic sunspot equilibrium deﬁned by Araujo and Maldonado (2000) are selected. Two examples are provided illustrating such reﬁnement process.