We experimentally investigate multiple notions of equity in ultimatum bargaining with asymmetric outside options. Building on the generalized equity principle formulated by Selten (1978), we derive three different equity rules that can explain 43% of all offers. Our within-subject design further allows us to show that proposers use different equity rules and apply them in a self-serving manner. They tend to follow the rules that suggest the highest payoff for them. Responders exhibit a similar pattern of behavior. Combined, these tendencies lead to high inefficiencies due to frequent rejections.