We propose reciprocal agents that self-organize associations based on cooperative relationships for efficient task/resource allocation problems in large-scale multi-agent systems (MASs). Computerized services are often provided by teams of networked intelligent agents by executing the corresponding tasks. However, performance in large-scale and busy MASs, may severely degrade due to conflicts because many task requests are excessively sent to a few agents with high capabilities. We introduce a game of N-agent team formation (TF game), which is an abstract form of the distributed allocation problem. We then introduce reciprocal agents that identifies dependable/trustworthy agents in TF games, shares the states between them, and preferentially works with them. Through this behavior with learning, they autonomously organize implicit associations that can considerably reduce conflicts and achieve fair reward distributions. We experimentally found that reciprocal agents could identify mutually dependable agents that formed independent associations, and efficiently team formed games. Finally, we investigated reasons for such efficient behaviors and found how their organizational structures emerged.