Effect of direct reciprocity and network structure on continuing prosperity of social networking services

Kengo Osaka, Fujio Toriumi, Toshihauru Sugawara

Social networking services (SNSs) are widely used as communicative tools for a variety of purposes. SNSs rely on the users' individual activities associated with some cost and effort, and thus it is not known why users voluntarily continue to participate in SNSs. Because the structures of SNSs are similar to that of the public goods (PG) game, some studies have focused on why voluntary activities emerge as an optimal strategy by modifying the PG game. However, their models do not include direct reciprocity between users, even though reciprocity is a key mechanism that evolves and sustains cooperation in human society. We developed an abstract SNS model called the reciprocity rewards and meta-rewards games that include direct reciprocity by extending the existing models. Then, we investigated how direct reciprocity in an SNS facilitates cooperation that corresponds to participation in SNS by posting articles and comments and how the structure of the networks of users exerts an influence on the strategies of users using the reciprocity rewards game. We run reciprocity rewards games on various complex networks and an instance network of Facebook and found that two types of stable cooperation emerged. First, reciprocity slightly improves the rate of cooperation in complete graphs but the improvement is insignificant because of the instability of cooperation. However, this instability can be avoided by making two assumptions: high degree of fun, i.e. articles are read with high probability, and different attitudes to reciprocal and non-reciprocal agents. We then propose the concept of half free riders to explain what strategy sustains cooperation-dominant situations. Second, we indicate that a certain WS network structure affects users' optimal strategy and facilitates stable cooperation without any extra assumptions. We give a detailed analysis of the different characteristics of the two types of cooperation-dominant situations and the effect of the memory of reciprocal agents on cooperation.