To address non-compliance, scholars controversially discuss which type of state - an incapable or an unwilling type - determines the structure of the game between an international organization and a state. Observational studies accordingly attempt to identify the dominance of one of the two types when they use conditional mean estimators, such as probit or logit, for a set of covariates, which describe the players' utilities. In this paper, we show that averaged effects can lead to biased or even false identification of state types. We introduce a strategic quantile model to reveal heterogeneous effects in strategic sequential games of compliance. Our re-examination of a compliance study demonstrates that both incapacity and unwillingness determine the structure of the strategic compliance game.