Compared with other species, exchange among non-kin is a hallmark of human sociality in both the breadth of individuals and total resources involved. One hypothesis is that extensive exchange evolved to buffer the risks associated with hominid dietary specialization on calorie dense, large packages, especially from hunting. 'Lucky' individuals share food with 'unlucky' individuals with the expectation of reciprocity when roles are reversed. Cross-cultural data provide prima facie evidence of pair-wise reciprocity and an almost universal association of high-variance (HV) resources with greater exchange. However, such evidence is not definitive; an alternative hypothesis is that food sharing is really 'tolerated theft', in which individuals possessing more food allow others to steal from them, owing to the threat of violence from hungry individuals. Pair-wise correlations may reflect proximity providing greater opportunities for mutual theft of food. We report a laboratory experiment of foraging and food consumption in a virtual world, designed to test the risk-reduction hypothesis by determining whether people form reciprocal relationships in response to variance of resource acquisition, even when there is no external enforcement of any transfer agreements that might emerge. Individuals can forage in a high-mean, HV patch or a low-mean, low-variance (LV) patch. The key feature of the experimental design is that individuals can transfer resources to others. We find that sharing hardly occurs after LV foraging, but among HV foragers sharing increases dramatically over time. The results provide strong support for the hypothesis that people are pre-disposed to evaluate gains from exchange and respond to unsynchronized variance in resource availability through endogenous reciprocal trading relationships.