An operational macroprudential approach to financial stability requires tools that attribute system-wide risk to individual institutions. Making use of constructs from game theory, we propose an attribution methodology that has a number of appealing features: it can be used in conjunction with popular risk measures, it provides measures of institutions’ systemic importance that add up exactly to the measure of system-wide risk and it easily accommodates uncertainty about the validity of the risk model. We apply this methodology to a number of constructed examples and illustrate the interactions between drivers of systemic importance: size, the institution’s risk profile and strength of exposures to common risk factors. We also demonstrate how the methodology can be used for the calibration of macroprudential capital rules.