Large parts of professional human communication proceed in a request-reply fashion, whereby requests contain specifics of the information desired while replies can deliver the required information. However, time limitations often force individuals to prioritize some while neglecting others. This dilemma will inevitably force individuals into defecting against some communication partners to give attention to others. Furthermore, communication entirely breaks down when individuals act purely egoistically as replies would never be issued and quest for desired information would always be prioritized. Here we present an experiment, termed "The expert game", where a number of individuals communicate with one-another through an electronic messaging system. By imposing a strict limit on the number of sent messages, individuals were required to decide between requesting information that is beneficial for themselves or helping others by replying to their requests. In the experiment, individuals were assigned the task to find the expert on a specific topic and receive a reply from that expert. Tasks and expertise of each player were periodically re-assigned to randomize the required interactions. Resisting this randomization, a non-random network of cooperative communication between individuals formed. We use a simple Bayesian inference algorithm to model each player's trust in the cooperativity of others with good experimental agreement. Our results suggest that human communication in groups of individuals is strategic and favors cooperation with trusted parties at the cost of defection against others. To establish and maintain trusted links a significant fraction of time-resources is allocated, even in situations where the information transmitted is negligible.