Primates spend a considerable amount of time grooming each other. Grooming is regularly found to be traded reciprocally (for grooming) or for rank-related benefits in the presence of food competition. It has been suggested that if food sources are clustered and monopolizable, then lower-ranked individuals will groom higher-ranked ones in order to be tolerated on food patches. This leads to grooming being directed up the hierarchy. However, the conditions where this is expected to occur are based on verbal reasoning alone, and no quantitative analysis of the conditions favouring grooming up the hierarchy appear in the literature. Here, we develop a quantitative model investigating when food competition can result in grooming up the hierarchy. Individuals are assumed to take actions pertaining to whom to groom, where to feed and whom to tolerate on food patches. By allowing individuals to choose actions according to reinforcement learning, we delineate conditions where groups of individuals will express reciprocal grooming and grooming up the hierarchy depending on environmental conditions (e.g. quality, number of food patches). In particular, we show that conditions of intense food competition may lead to less grooming up the hierarchy. The predictions of our model could guide future comparative studies and meta-analyses investigating social relationships in primates.