We report results from a laboratory experiment on strategic bargaining with indivisibilities studying the role of asymmetries, both in preferences and institutions. We find that subjects do not fully grasp the equilibrium effects asymmetries have on bargaining power and identify how subjects’ observed behavior systematically deviates from theoretical predictions. The deviations are especially pronounced in case of asymmetric institutions which are modelled as probabilities of being the proposer. Additionally, in contrast to previous experimental work, we observe larger than predicted proposer power since subjects frequently propose and accept their second-preferred option. Quantal response equilibrium and risk aversion explain behavior whenever probabilities are symmetric, but less so when asymmetric. We propose the ‘recognition is power’ heuristic which equates bargaining power with recognition probabilities to explain these findings.