The evolution in animals of a first possession convention, in which individuals retain what they are the first to acquire, has often been taken as a foundation for the evolution of human ownership institutions. However, among humans, individuals actually only seldom retain an item they have acquired from the environment, instead typically transferring what they possess to other members of the community, to those in command, or to those who hold a contractual title. This paper presents a novel game-theoretic model of the evolution of ownership institutions as rules governing resource transfers. Integrating existing findings, the model contributes a new perspective on the emergence of communal transfers among hominin large game hunters around 200,000 years ago, of command ownership among sedentary humans in the millennia prior to the transition to agriculture, and of titled property ownership around 5,500 years ago. Since today's property institutions motivate transfers through the promise of future returns, the analysis presented here suggests that these institutions may be placed under considerable pressure should resources become significantly constrained.