In this essay I argue that one can understand the relationship between those who rule and those who are ruled in civil society as an implicit contractual relationship or contract by convention. I use variations of the extensive form Trust Game to summarize the structures of alternative forms of contracts, and apply these variations to model the relationship between the rulers and those under their rule. One of these variations, the Irrevocable Sovereignty Game, summarizes Hobbes‘ main argument for why it is conceptually impossible for a contract to exist between a sovereign and the subjects under its rule. I argue that Hobbes‘ argument presupposes a common understanding of a contract as a set of promises enforceable by a third party, such as a legally binding agreement. I use another variation of the Trust Game, the Repeatable Sovereignty Game, to show that rulers and ruled can establish and maintain a convention requiring the ruled to obey their rulers‘ commands in return for these rulers providing the ruled satisfactory benefits. In effect, the ruled and their rulers create an implicit contract that is self-enforcing rather than an explicit contract requiring third-party enforcement. I argue that this idea of a governing convention has roots in David Hume’s discussions of government, and is even implicit in Hobbes‘ own treatment of sovereignty.