Influential thinkers such as Young, Sugden, Binmore, and Skyrms have developed game-theoretic accounts of the emergence, persistence and evolution of social contracts. Social contracts are sets of commonly understood rules that govern cooperative social interaction within societies. These naturalistic accounts provide us with valuable and important insights into the foundations of human societies. However, current naturalistic theories focus mainly on how social contracts solve coordination problems in which the interests of the individual participants are (relatively) aligned, not competition problems in which individual interests compete with group interests (and in which there are no group beneficial Nash equilibrium available). In response, I set out to build on those theories and provide a (more) comprehensive naturalistic account of the emergence, persistence and evolution of social contracts. My central claim is that social contracts have culturally evolved to solve cooperation problems, which include both coordination and competition problems. I argue that solutions to coordination problems (which I spell out) emerge from “within-group” dynamics, while solutions to competition problems (which I also spell out) result largely from “between-group” dynamics.