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.

中文翻译：

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直接互惠和网络结构对社交网络服务持续繁荣的影响。

社交网络服务 (SNS) 被广泛用作各种用途的交流工具。SNS 依赖于与一些成本和努力相关的用户个人活动，因此不知道为什么用户自愿继续参与 SNS。由于 SNS 的结构类似于公共物品 (PG) 博弈的结构，因此一些研究集中在为什么通过修改 PG 博弈来将志愿活动作为最优策略出现。然而，他们的模型不包括用户之间的直接互惠，尽管互惠是人类社会发展和维持合作的关键机制。我们开发了一个抽象的 SNS 模型，称为互惠奖励和元奖励游戏，通过扩展现有模型包括直接互惠。然后，我们研究了 SNS 中的直接互惠如何通过发布文章和评论来促进与参与 SNS 相对应的合作，以及用户网络的结构如何影响使用互惠奖励游戏的用户的策略。我们在各种复杂网络和 Facebook 的一个实例网络上运行互惠奖励游戏，发现出现了两种类型的稳定合作。首先，互惠性略微提高了完全图中的合作率，但由于合作的不稳定性，这种改善并不显着。然而，这种不稳定性可以通过做两个假设来避免：高度有趣，即文章以高概率被阅读，以及对互惠和非互惠代理的不同态度。然后，我们提出半搭便车的概念来解释什么策略可以维持合作主导的情况。其次，我们指出特定的 WS 网络结构会影响用户的最优策略，并在没有任何额外假设的情况下促进稳定的合作。我们详细分析了两种合作主导情境的不同特征以及互惠主体的记忆对合作的影响。