Imitators and optimizers in a changing environment

We analyze the repeated interaction between an imitating and a myopically optimizing player in an otherwise symmetric environment of changing marginal payoff. Focusing on finite irreducible environments and the case of strategic substitutes, we unfold a trade-off between the degree of interaction and the size of environmental shocks. The optimizer outperforms the imitator if interaction is weak or shocks are large. As to the case of duopoly, this translates into small cross-price elasticities or large shocks in marginal cost and/or the maximum willingness to pay. In these cases, a changing environment creates selection pressure against imitative behavior.