In the awarded paper, I proposed a formal model that synthesized the emancipation theory of trust and some criticisms on the theory. In this paper, I explain the implication of the awarded paper, especially on the multilayeredness and multiplicity of social networks and on the cusp catastrophe model, and subsequently argue the potentiality of the multilevel social network model in mathematical sociology.

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     Social capital theorists say that reputations circulate in dense and highly homogeneous social networks. However, Yamagishi (1998) distinguishes the trust to specified others from the trust to unspecified ones. He points out that such a reputation cannot promote cooperation toward unspecified others. I built a model based on Macy & Sato (2002), assuming that a network was modified by the reputations via one-step neighbors. I analyze the relation between cooperation to general others and opportunity costs. As a result, when opportunity costs are extremely small, a star-type network tends to be formed, and social order to cooperate to unspecified others is generated by agents who can access many reputations. It also became clear that when opportunity costs are extremely large, market-shaped order is generated from reputations.

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     We investigated the effect of tolerance of reputation-making norms on cooperation by conducting an evolutionary simulation with more realistic constraints than those in previous studies. Specifically, agents could make social exchanges only within their neighborhoods on the network, and could refer to the reputation of others only within two steps on the network when exchanging and rewiring. Under these constraints, we compared the effect of three reputation-making norms which varied across the levels of tolerance: i.e., image scoring, standing, and strict discriminator. The results were as follows. Under the standing norm, while social exchanges increased in number because the network became dense, cooperation was highly likely to collapse because defection tended to be more adaptive than cooperation. On the other hand, under the strict discriminator norm, while cooperation was stable, the social exchanges decreased in number because the network became sparse. These results indicate that the tolerances of reputation-making norms would affect not only the robustness of cooperation but also the structure of the social network. This implies that the intolerant reputation-making norm focusing only on level of cooperation may have negative effects on social capital by shrinking the social network as a by-product. In the second simulation, we added perceptual errors that caused agents to misinterpret another's reputation. The results showed that the cooperation was stable even under tolerant standing norm. This implies that when social exchanges are done under the constraints of the network structure and perceptual errors, even the tolerant reputation-making norm can maintain cooperation.

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     How can people overcome their differences to form a large group? This study addressed this question with an agent-based computer simulation in which individuals are loosely connected in a group. This model revises the Schelling Model (Schelling 1971), in which agents move away from neighbors with different traits, as well as the Axelrod Model (Axelrod 1997), in which agents with diverse features and traits interact with one another. Our model defines a community as the largest group operating during any of the steps in the entire simulation. The question of interest was what types of agents contribute to the formation of large communities when the agents are given various features (F) and traits (Q). The following conclusions emerged from our data. When the ratio of Q/F was low, “modest” agents, who tried to form a group with neighbors with whom they shared the fewest features, contributed most to establishing larger communities. When the ratio of Q/F was high, “moving” agents, who tried to distant from neighbors with different traits, contributed most to forming larger communities. Moving agents contributed more to the formation of large communities as the length of the simulation increased. These results suggest that “strangers/outsiders” who migrate between groups contribute to community formation when mismatches among agents are most pronounced. This paper thus supports the theoretical significance of the objectivity of strangers/outsiders in the domain of sociology.

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     This paper presents an agent based model to simulate the process of formation of culture considering the adaptation to the environmental condition and discuss the effect of dynamic change of social network.
     In the presented model, agents learn the information provided from the environment and agents do not simply share the information that was hold by agents at the initial state. In the diffusion process of information, agents do not simply copy other agents' state variables, but share the target of learning, which is supposed to simulate “conditional learning”. Network is supposed to be dynamic and links are rewired based on the homophily rule. Dynamic analysis of the model is supposed to show the co-evolution process of network and culture.
     Simulation results reveal that several groups of culture, which are corresponding to the environmental conditions, are formed when homophilic property of network dynamics is suppressed by constraint on the link rewiring, etc. These results indicate a new mechanism of formation of polarized cultural groups in the community, society and so forth.

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     We have analyzed the effects of spatial and social distance on a friendship network. We used the data obtained from “Tomocom” which is a social network service where approximately 350 undergraduate students living in several areas in Japan are participating. From the data, we have found that spatial and social distance between individuals causes stratification in the friendship network and brings about nested structure of small world. Based on what we have found in the data analysis, we have built a model and successfully replicated the nested structure of small world in the simulation.

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     This paper extends the Garbage Can Model of Cohen et al. (1972) by introducing network structures between participants and its dynamics. Given a network structures, if there are large communication costs among participants, then the network structure affects the efficiency of organizations. In this case, participants occupying more central positions have more experiences of solving problems. In contrast, network structures that impose no communication costs have lesser influence on efficiency, and participants occupying more central positions have less experiences of solving problems. Such a situation affects the result of the dynamics of network formation. Large communication costs promote the formation of multiple centered stars, with the number of centers depending on the maximum number of links that participants can form. In contrast, network structures that impose no communication costs promote the formation of only one or two centers, but even if two participants have the same large number of links, one participant has the highest experience of solving problems and the other has the lowest one. Thus, when experience of solving problems increases network participants' reputations in the organization, the situation arises that participants having the same social capital have differing reputations. This difference arises from the organization's social condition and social dynamics, even if homogeneous agents are assumed.

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     A matching theory provides the perspective on the resource allocation or exchange of indivisible goods under the competitive condition. Most of the recent work in economics has concentrated on the question of how a policy maker or social planner should design the matching algorithm from the viewpoint of stability, Pareto efficiency, and strategy-proofness.
     By contrast, the current study treats matching algorithm as the rule of social interactions, not as just a calculation process and focuses on social inequality of the resulting matching outcome. We construct a model in which players are located on social network. The players chose other linked player as their partner according to the rule resembling Gale-Shapley's Deferred Acceptance algorithm and then share their ability or resources with their partner. We assume that the resource of unmatched player (called “excluded player”) is discounted. Under this condition, we investigate how the structure of social networks affects the degree of social inequality and what type of player pair with what type of partner through computer simulation. The simulation shows that the social networks whose variance of degree is higher exacerbate society-wide inequality even though they limit the inequality gap only among the matched players. Additionally, we find that the more players have links, the more capable partner they can pair with.
     The empirical implications and the contribution of our framework to normative theory are also discussed.

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     The purpose of this paper is to show the features of agent-based model and discuss its progress in sociology. First, this paper will show the features of agent-based model with comparison to the traditional methods in sociology such like mathematical modeling and quantitative analysis. Next, this paper will confirm the progress of agent-based model in sociology, reviewing topics such as (a) the emergence of social order and (b) the emergence of social structure. Last, this paper will discuss the topic which is important in sociology but unexplored in agent-based model.

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     This paper applies Bourdieu's social space approach to Japanese data, where two theses proposed in Distinction, that is, a ‘chiastic structure’ of a social space and ‘homology’ between it and behavior/opinion spaces are examined. Data from the 2005 SSM survey are analyzed by multiple correspondence analysis (MCA) and a Euclidean classification of individuals. The analysis reveals that differences by ‘volume of capital’ appear clearly both in social and behavior/opinion spaces but differences by ‘composition of capital’ are unexpectedly small in the former space and are quite unclear in the latter spaces. Through these analyses, effectiveness of a social space approach in class and stratification research is suggested as well as characteristics of Japanese social space.

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     This paper examines whether and how educational expansion affects inequality of educational opportunity, focusing on the two hypotheses which argue that educational expansion transforms class inequality through saturation of education. Under the condition that a level of education approaches nearly saturation, the MMI hypothesis claims class inequality in attaining the level of education begins to decrease and the EMI hypothesis maintains class inequality over types within the level of education emerges. Taiwan and Japan showed similarity in educational system, but education in Taiwan has expanded more drastically than that in Japan. To test the hypotheses, utilizing their different time point in appearance of saturation caused by the respective pace of expansion, we present the expectations on changes in class inequality for the two countries. The result of analysis using survey data collected in each country is more consistent with the MMI rather than the EMI. Class inequality in attaining levels of education persisted until approaching saturation, but reduced in attaining senior high school education in Japan when this level of education reached saturation. Class inequality in attaining university education rather than junior college over types of higher education emerged clearly corresponding to approaching saturation in Taiwan but appeared in Japan before saturation. The result also indicates that educational expansion urges the transformation of class inequality and gender inequality through respective process. Educational expansion leads to reduction of gender inequality in attaining levels of education irrespective of rapidity and saturation of expansion and without interaction by class and gender in both countries, but hardly erodes gender-specific educational paths institutionalized by gender norm or preference preserved in Japan.

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     This paper provides a survey of the key thematic and methodological milestones in research into educational inequalities. The article focuses on authors and concepts that introduced major innovations and contributed to significant advancements in the analysis and knowledge of educational inequalities. We have distinguished three periods, focusing on two key concepts in each. The first period is represented by the basic model of the process of stratification and the social-psychological model. The second period includes the educational allocation concept and the theory of maximally maintained inequality (MMI). Finally, the third period is described on the grounds of the multinomial transition model and the theory of effectively maintained inequality (EMI). Across these development stages, three of the above-mentioned concepts are presented as breakthrough methodological innovations while another three concepts are viewed as thematic (interpretational) innovations, closely linked to the development of quantitative methods used to analyse educational inequalities.

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