This paper proposes and analyzes a model of strategic behavior under counterfactual explanations. In this model, a decision-maker chooses a policy and a small set of explanations that can be provided to decisions subjects who receive unfavorable decisions. In response, decision subjects follow the given explanation to improve their future outcomes. While doing so is NP Hard, the resulting formulation is shown to be submodular allowing for efficient approximations. This paper establishes an interesting connection between strategic behavior and explainability. While the paper makes some interesting contributions, it has the following weaknesses: 1) Certain notions are not well defined -- "beneficial decision" vs. "positive prediction" 2) Actual algorithms pushed to appendix 3) Strong assumptions are being made -- e.g., only considering decision-maker utility as opposed to social welfare/decision subjects' utility; assuming decision-maker knows the true probabilistic relationship between features and outcomes. We would encourage the authors to address the aforementioned aspects in their final version.