Recent improvements in program evaluation techniques have allowed researchers to estimate the spillover effects of programs and policies, in addition to the direct effects. However, in some settings, there may be an interaction between the direct effects and the spillover effects of a treatment if the size of spillovers depends on an individual’s own treatment status. These interactions are strategic if an individual’s treatment status depends on the treatment of their neighbors. This paper shows that, in the presence of strategic interactions, reduced form estimates of direct effects are biased, even when a ‘randomized saturation’ experimental design is used. We propose a two-step procedure to test for and correct this bias. The first step is a simple regression-based test for strategic interactions. Conditional on finding evidence of strategic interactions, the second step uses a simple, parsimonious model adapted from Acemoglu, Garcia-Jimeno and Robinson (2015) to estimate the underlying structural parameters and effects of treatment. When the treatment variable is continuous, the second step involves joint estimation of two linear equations. However, when treatment is binary, the approach requires a Heckman-style selection bias correction because individuals can choose whether or not to comply with their assignment to treatment. We demonstrate our procedure using simulated data and apply it to data from two empirical papers. We find no evidence of strategic interactions in decisions to attend a job market training program in France. However, we do find evidence of strategic interactions in decisions to receive deworming treatment in Kenya, and use our model to estimate the structural parameters, and the corresponding direct and spillover effects of treatment.