This note used the terminology and notation of Ross . The example presented here is a denumerable Markovian decision process which has an optimal nonstationary rule which is better than every stationary rule. This answers a question of Derman .
Lloyd Fisher. Sheldon M. Ross. "An Example in Denumerable Decision Processes." Ann. Math. Statist. 39 (2) 674 - 675, April, 1968. https://doi.org/10.1214/aoms/1177698426