AbstractPermissionless blockchains require a protocol to generate consensus. Many prominent permissionless blockchains employ Proof-of-Work (PoW) for that purpose, but PoW possesses significant shortcomings. Various alternatives have been proposed. This paper provides the first formal economic model of the most famous alternative, Proof-of-Stake (PoS), and establishes conditions under which PoS generates consensus. A sufficiently modest reward schedule not only implies the existence of an equilibrium in which consensus obtains as soon as possible but also precludes a persistent forking equilibrium. The latter result arises because PoS, unlike PoW, requires that validators are also stakeholders.