'Simple' hunter-gatherer populations adopt the social norm of 'demand sharing', an example of human hyper-cooperation whereby food brought into camps is claimed and divided by group members. Explaining how demand sharing evolved without punishment to free riders, who rarely hunt but receive resources from active hunters, has been a long-standing problem. Here we show through a simulation model that demand-sharing families that continuously move between camps in response to their energy income are able to survive in unpredictable environments typical of hunter-gatherers, while non-sharing families and sedentary families perish. Our model also predicts that non-producers (free riders, pre-adults and post-productive adults) can be sustained in relatively high numbers. As most of hominin pre-history evolved in hunter-gatherer settings, demand sharing may be an ancestral manifestation of hyper-cooperation and inequality aversion, allowing exploration of high-quality, hard-to-acquire resources, the evolution of fluid co-residence patterns and egalitarian resource distribution in the absence of punishment or warfare.