Among non-human animals, a key strategy to resolve conflicts without fighting relies on assessing relative fighting ability on the basis of physical cues such as size and strength. Recent studies hypothesize that the human mind also contains mechanisms for spontaneously coordinating conflict behavior on the basis of difference in physical strength, even if strength is not rationally relevant to the conflict. We provide the first direct, experimental test of the existence of such mechanisms. We do so by applying a non-physical, anonymous, economic game - the war-of-attrition - in which male contestants compete by means of perseverance to win a monetary prize. While initial studies provided some support for the prediction, the final well-powered and pre-registered study failed to support the prediction. Overall, we interpret our findings as evidence against the hypothesis that the human mind attributes relevance to physical factors that are irrelevant for the actual resolution of a conflict. We discuss implications for existing findings in the field and provide directions for further research.