Classification algorithms are increasingly important in areas such as obtaining credit, employment, health care, housing, law enforcement, and national security. These classification decisions affect peoples’ lives and, accordingly, can shape their behaviors. We present a formal model of optimal classification by an algorithm designer who may want to affect the distribution of behavior in a population. Our model allows the designer to have a wide array of objectives (such as maximizing compliance or maximizing accuracy, among many others) and these objectives shape equilibrium behavioral outcomes in the population, sometimes in surprising ways. Our results speak to questions of algorithmic fairness in settings where behavior and algorithms are interdependent, and where typical measures of fairness focusing on statistical accuracy across groups may not be appropriate.