People need to rely on cooperation with other individuals in many aspects of everyday life, such as teamwork and economic exchange in anonymous markets. We study whether and how the ability to make or break links in social networks fosters cooperate, paying particular attention to whether information on an individual's actions is freely available to potential partners. Studying the role of information is relevant as information on other people's actions is often not available for free: a recruiting firm may need to call a job candidate's references, a bank may need to find out about the credit history of a new client, etc. We find that people cooperate almost fully when information on their actions is freely available to their potential partners. Cooperation is less likely, however, if people have to pay about half of what they gain from cooperating with a cooperator. Cooperation declines even further if people have to pay a cost that is almost equivalent to the gain from cooperating with a cooperator. Thus, costly information on potential neighbors' actions can undermine the incentive to cooperate in fluid networks.