Given the ubiquity of AI-based decisions that affect individuals' lives, providing transparent explanations about algorithms is ethically sound and often legally mandatory. How do individuals strategically adapt following explanations? What are the consequences of adaptation for algorithmic accuracy? We simulate the interplay between explanations shared by an Institution (e.g. a bank) and the dynamics of strategic adaptation by Individuals reacting to such feedback. Our model identifies key aspects related to strategic adaptation and the challenges that an institution could face as it attempts to provide explanations. Resorting to an agent-based approach, our model scrutinizes: i) the impact of transparency in explanations, ii) the interaction between faking behavior and detection capacity and iii) the role of behavior imitation. We find that the risks of transparent explanations are alleviated if effective methods to detect faking behaviors are in place. Furthermore, we observe that behavioral imitation - as often happens across societies - can alleviate malicious adaptation and contribute to accuracy, even after transparent explanations.