As a method of analyzing and predicting social phenomena using social media as data, we present analyses based on the mathematical model of the hit phenomenon, which is one of the established models of sociophysics. The dynamics of the number of social media posts for movies, events, and a YouTube movie are explained. For entertainment topics, the direct communication strength, “D,” indicates the satisfaction of the current interested people or supporters, whereas the indirect communication strength, “P,” indicates the power to acquire a new support layer. Thus, this is effective not only for the analysis of entertainment and marketing strategy but also for burst analysis on the social media.

Income redistribution is a feasible means to adjust the income among individuals, which could reduce the gap between the rich and the poor and realize the social equity. By means of taxation and public services, the income could be transferred from some individuals to others directly or indirectly. We study how income redistribution affects the evolution of global cooperation through proposing a multi-level threshold public goods game model and introducing two kinds of income redistribution mechanisms. We find that both of the income redistribution mechanisms promote global cooperation. Furthermore, the global income redistribution is more in favor of the emergence of global cooperative behaviors than the local income redistribution mechanism. On the other hand, the fixation time of global cooperation is sharply shortened after introducing income redistribution mechanisms. In threshold public goods games, only when the amount of collected public goods reaches a certain threshold, the income of individuals can be guaranteed. Hence, the influences of thresholds of different levels on strategies are investigated in the paper.

In social evolution theory, unconditional cooperation has been seen as an evolutionarily unsuccessful strategy unless there is a mechanism that promotes positive assortment between like individuals. One such example is kin selection, where individuals sharing common ancestry and therefore having the same strategy are more likely to interact with each other. Conditional cooperation, on the other hand, can be successful if interactions with the same partners last long. In many previous models, it has been assumed that individuals act conditionally on the past behavior of others. Here I propose a new model of conditional cooperation, namely the model of coordinated cooperation. Coordinated cooperation means that there is a negotiation before an actual game is played, and that each individual can flexibly change their decision, either to cooperation or to defection, according to the number of those who show the intention of cooperation/defection. A notable feature of my model is that individuals play an actual game only once but can still use conditional strategies. Since such a negotiation is cognitively demanding, the target of my model here is exclusively human behavior. I have analyzed cultural evolutionary dynamics of conditional strategies in this framework. Results for an infinitely large population show that conditional cooperation not only works as a catalyst for the evolution of cooperation, but sustains a polymorphic attractor with unconditional cooperators, unconditional defectors, and conditional cooperators being present. A finite population analysis is also performed. Overall, my results provide one explanation of why people tend to take into account others' decisions even when doing so gives them no payoff consequences at all.

Many phenomena with power laws have been observed in various fields of the natural and social sciences, and these power laws are often interpreted as the macro behaviors of systems that consist of micro units. In this paper, we review some basic mathematical mechanisms that are known to generate power laws. In particular, we focus on stochastic processes including the Yule process and the Simon process as well as some recent models. The main purpose of this paper is to explain the mathematical details of their mechanisms in a self-contained manner.

Indirect reciprocity is one of the basic mechanisms to sustain mutual cooperation, by which beneficial acts are returned, not by the recipient, but by third parties. This mechanism relies on the ability of individuals to know the past actions of others, and to assess those actions. There are many different systems of assessing others, which can be interpreted as rudimentary social norms (i.e., views on what is “good” or “bad”). In this paper, impacts of different adaptive architectures, i.e., ways for individuals to adapt to environments, on indirect reciprocity are investigated. We examine two representative architectures: one based on replicator dynamics and the other on genetic algorithm. Different from the replicator dynamics, the genetic algorithm requires describing the mixture of all possible norms in the norm space under consideration. Therefore, we also propose an analytic method to study norm ecosystems in which all possible second order social norms potentially exist and compete. The analysis reveals that the different adaptive architectures show different paths to the evolution of cooperation. Especially we find that so called Stern-Judging, one of the best studied norms in the literature, exhibits distinct behaviors in both architectures. On one hand, in the replicator dynamics, Stern-Judging remains alive and gets a majority steadily when the population reaches a cooperative state. On the other hand, in the genetic algorithm, it gets a majority only temporarily and becomes extinct in the end.