Sexual conflict arises whenever males and females have divergent reproductive interests. The mechanisms mediating the resolution of sexual conflict have been studied extensively in the context of parental care, where each parent adjusts its decision about how much care to provide based on its partner's workload. However, there is currently no information on the mechanisms mediating the resolution of sexual conflict over personal consumption from a shared resource. We address this gap in the burying beetle Nicrophorus vespilloides, which breeds on small vertebrate carcasses. The carcass serves as a source of food for both the developing larvae and the caring parents, and parents feed from the carcass for self-maintenance. To study the mechanisms mediating conflict resolution, we experimentally varied the two parents' body size to create variation in carcass consumption. We then assessed whether each parent adjusted its consumption based on its own size, its partner's size and its partner's consumption. As expected, large parents gained more mass than small parents. Furthermore, males paired to large females gained more mass than males paired to small females, and females responded to their partner's mass change, gaining more mass when their partner did. Our study provides insights into the resolution of a new form of sexual conflict, showing that it is mediated through both matching and sealed-bid responses. Our findings also suggest that the resolution models developed in the context of sexual conflict over biparental care may apply more generally than previously thought.