Adversarial training aims to defend against *adversaries*: malicious opponents whose sole aim is to harm predictive performance in any way possible - a rather harsh perspective, which we assert results in unnecessarily conservative models. Instead, we propose to model opponents as simply pursuing their own goals, rather than working directly against the classifier. Employing tools from strategic modeling, our approach uses knowledge or beliefs regarding the opponent's possible incentives as inductive bias for learning. Our method of *strategic training* is designed to defend against opponents within an *incentive uncertainty set*: this resorts to adversarial learning when the set is maximal, but offers potential gains when it can be appropriately reduced. We conduct a series of experiments that show how even mild knowledge regarding the adversary's incentives can be useful, and that the degree of potential gains depends on how incentives relate to the structure of the learning task.