What drove the transition from small-scale human societies centred on kinship and personal exchange, to large-scale societies comprising cooperation and division of labour among untold numbers of unrelated individuals? We propose that the unique human capacity to negotiate institutional rules that coordinate social actions was a key driver of this transition. By creating institutions, humans have been able to move from the default 'Hobbesian' rules of the 'game of life', determined by physical/environmental constraints, into self-created rules of social organization where cooperation can be individually advantageous even in large groups of unrelated individuals. Examples include rules of food sharing in hunter-gatherers, rules for the usage of irrigation systems in agriculturalists, property rights and systems for sharing reputation between mediaeval traders. Successful institutions create rules of interaction that are self-enforcing, providing direct benefits both to individuals that follow them, and to individuals that sanction rule breakers. Forming institutions requires shared intentionality, language and other cognitive abilities largely absent in other primates. We explain how cooperative breeding likely selected for these abilities early in the Homo lineage. This allowed anatomically modern humans to create institutions that transformed the self-reliance of our primate ancestors into the division of labour of large-scale human social organization.