Photoinhibition is characterised by a decreasing rate of photosynthesis with increasing light. It occurs in many photosynthetic organisms and is especially apparent in phytoplankton species sensitive to high light. Yet, the population and community level consequences of photoinhibition are not well understood. Here, we present a resource competition model that includes photoinhibition. The model shows that, in strong light, photoinhibition leads to an increase of the specific growth rate with increasing population density due to self-shading. This so-called Allee effect can be either weak or strong. In monoculture, a strong Allee effect results in two alternative stable states. A low population density does not provide sufficient shade to protect itself against photoinhibition, such that the population goes extinct. Conversely, above a threshold population density the population may create sufficiently turbid conditions to suppress photoinhibition, so that the population can establish itself. When several species compete for light, a species which cannot establish itself due to photoinhibition can be facilitated by other species less sensitive to photoinhibition. If such facilitators are absent, photoinhibition may cause alternative stable states in community composition. Since each alternative stable state is dominated by a single species, photoinhibition does not favour species coexistence. The model predictions are consistent with published competition experiments, and illustrate the complex effects of photoinhibition on community assembly.