Brand imitation is a common practice that can take different forms, i.e., legal copying, as in the case of clones and knockoffs, or illegal, in the case of counterfeiting. We consider a scenario in which a producer enters the market with a "similar" product to the incumbent's and we assess the impact of this entry on the incumbent's strategies and outcomes. A distinctive feature of our model is that it allows for brand dilution, which means that the original brand suffers due to imitation, and for brand enhancement, when the availability of the imitation product actually promotes the original brand.

We characterize and contrast the solutions for the scenario with entry and the benchmark case where no entry occurs, in a fully dynamic context.