Although positive incentives for cooperators and/or negative incentives for free-riders in social dilemmas play an important role in maintaining cooperation, there is still the outstanding issue of who should pay the cost of incentives. The second-order free-rider problem, in which players who do not provide the incentives dominate in a game, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players’ incentives. The critical assumption of our model is that players who tend to provide incentives to other players for their cooperative or non-cooperative behavior also tend to provide incentives to their incentive behaviors. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We find that the second-order free-rider problem is completely resolved without any third-order or higher (meta) incentive under the assumption. To do so, a second-order costly incentive, which is given individually (peer-to-peer) after playing donation games, is needed. The paper concludes that (1) second-order incentives for first-order reward are necessary for cooperative regimes, (2) a system without first-order rewards cannot maintain a cooperative regime, (3) a system with first-order rewards and no incentives for rewards is the worst because it never reaches cooperation, and (4) a system with rewards for incentives is more likely to be a cooperative regime than a system with punishments for incentives when the cost-effect ratio of incentives is sufficiently large. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives. Although social dilemmas can be resolved if punishing non-cooperators or rewarding cooperators works, such rewards and punishments, i.e., external incentives, entail certain expenses. As a result, a cooperative player who shirks his or her duty to provide an incentive to other players will emerge, and he or she will be more advantageous than an incentive-provider. In fact, the problem of excluding such cooperative incentive-non-providers, or second-order free-riders, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players’ incentives. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We show that second-order incentives for first-order reward are necessary for cooperative regimes. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives.

Although various norms for reciprocity-based cooperation have been suggested that are evolutionarily stable against invasion from free riders, the process of alternation of norms and the role of diversified norms remain unclear in the evolution of cooperation. We clarify the co-evolutionary dynamics of norms and cooperation in indirect reciprocity and also identify the indispensable norms for the evolution of cooperation. Inspired by the gene knockout method, a genetic engineering technique, we developed the norm knockout method and clarified the norms necessary for the establishment of cooperation. The results of numerical investigations revealed that the majority of norms gradually transitioned to tolerant norms after defectors are eliminated by strict norms. Furthermore, no cooperation emerges when specific norms that are intolerant to defectors are knocked out.

Why do people use social media, even though they must pay certain costs for generating content? The purpose of this study is to answer a more pointed question: What type of mechanism can encourage the continuous participation of users in social media? To address this question, we clarify various conditions that must be met to motivate users to voluntarily provide information in social media. In this work, we use the framework of ``the public goods game'' to describe user behaviors such as posting articles and comments. We first describe the communication carried out in specific social media by extending the metanorms game, which issues both rewards for cooperation and punishments for non-cooperation. We further develop a simulation model to clarify the conditions needed to create a cooperation-dominant environment, which we define as a world where nearly everyone cooperates in the sense used in game theory. From the results of our agent-based simulation, it is clear that the rewards for cooperation and the rewards for rewards given by others can work to encourage cooperation. Furthermore, we analyze the relationships between the costs and benefits of cooperation by using dynamics analysis. Consequently, we clarify that cooperative behaviors are dominant when the benefits of cooperation are larger than the costs of rewarding other users.

Indirect reciprocity is one of the major mechanisms in the evolution of human cooperation. In indirect reciprocity, social norms with which individuals distinguish good people from bad people play essential roles. Despite extensive studies on the evolution of cooperation in indirect reciprocity, little is known about which social norms people actually adopt. Here we reveal what kind of norms are adopted by people in indirect reciprocal situations in daily life by using scenario-based experiments. The results showed that people evaluated “justified defection” as neither good nor bad and withheld their evaluation. Theoretically, social norms that evaluate justified defection as good are required for cooperation to be stable. However, the norm that people actually adopted deviates from the theoretical predictions. Our results indicate the necessity to reconsider the justification of “justified defection” in the evolution of cooperation.