Cooperative behaviors are common in humans and are fundamental to our society. Theoretical and experimental studies have modeled environments in which the behaviors of humans, or agents, have been restricted to analyze their social behavior. However, it is important that such studies are generalized to less restrictive environments to understand human society. Social network games (SNGs) provide a particularly powerful tool for the quantitative study of human behavior. In SNGs, numerous players can behave more freely than in the environments used in previous studies; moreover, their relationships include apparent conflicts of interest and every action can be recorded. We focused on reciprocal altruism, one of the mechanisms that generate cooperative behavior. This study aims to investigate cooperative behavior based on reciprocal altruism in a less restrictive environment. For this purpose, we analyzed the social behavior underlying such cooperative behavior in an SNG. We focused on a game scenario in which the relationship between the players was similar to that in the Leader game. We defined cooperative behaviors by constructing a payoff matrix in the scenario. The results showed that players maintained cooperative behavior based on reciprocal altruism, and cooperators received more advantages than noncooperators. We found that players constructed reciprocal relationships based on two types of interactions, cooperative behavior and unproductive communication.