We study the extent to which cooperative behavior can be sustained in anonymous,
evolving social networks, such as online communities. Individuals strategically
form relationships under a social matching protocol and engage in prisoner’s dilemma
interactions with their partners. An agent that defects escapes direct reciprocity by
virtue of anonymity: when starting a new relationship, neither agent has available
any information about the history of his partner. We demonstrate that cooperation
is sustainable at equilibrium in such a model, and characterize a class of equilibria
that support cooperation as a stationary outcome. The endogenous dynamics of the
social network imply that cooperation allows an individual to interact with a growing
number of other cooperators over time, potentially balancing the immediate gains from
defection.