Typical accounts of the ability of social networks to enable collective action focus on either whole group or individual advantages. Adding an intermediate perspective, this paper advances a core notion of strategic embeddedness that applies to social interactions involving a subset of society. Strategic embeddedness is modeled with a game-theoretic approach that places an otherwise isolated game into a broader social structure. To facilitate a comparative institutional analysis of formal and informal mechanisms, this paper advances a complementary notion of the cooperative value of a network to evaluate the maximum payoffs possible under various network structures that define the social context of two-person cooperation games. A formal analysis indicates that decentralized network structures can maximize this cooperative value: under some conditions, these are both optimal and efficient structures that can effectively substitute for anonymous public enforcement mechanisms. In conditions where private enforcement is relatively ineffective vis-a-vis a public rule of law enforcement mechanism, then hierarchical network structures are shown to be optimal but inefficient. In general, more connectedness or a higher network density does not readily translate into more cooperation because when most players are connected to the rest of society, the added value of social networks diminishes in the absence of extraneous rules to discriminate among players with common social connections.