Since Robbins (1956), a large literature has evolved treating the empirical Bayes formulation of a sequence of decision problems. In this paper we look at the formulation and the asymptotic optimality criterion as a classical iid problem and a consistency property. With this point of view and the finite state component problem, we evoke classical results on Bayes procedures to prove a complete class theorem and to establish the asymptotic optimality of Bayes empirical Bayes procedures.
"Bayes Empirical Bayes: Finite Parameter Case." Ann. Statist. 10 (4) 1277 - 1282, December, 1982. https://doi.org/10.1214/aos/1176345993