Understanding the mechanisms of network formation is central in social network analysis. Network formation has been studied in many research fields with their different focuses; for example, network embedding algorithms in machine learning literature consider broad heterogeneity among agents while the social sciences emphasize the interpretability of link formation mechanisms. Here we propose a social network formation model that integrates methods in multiple disciplines and retain both heterogeneity and interpretability. We represent each agent by an "endowment vector" that encapsulates their features and use game-theoretical methods to model the utility of link formation. After applying machine learning methods, we further analyze our model by examining micro- and macro- level properties of social networks as most agent-based models do. Our work contributes to the literature on network formation by combining the methods in game theory, agent-based modeling, machine learning, and computational sociology. Network formation has been studied in many research fields with their different focuses; for example, network embedding algorithms in machine learning literature consider broad heterogeneity among agents while the social sciences emphasize the interpretability of link formation mechanisms. Here we propose a social network formation model that integrates methods in multiple disciplines and retain both heterogeneity and interpretability. We represent each agent by an “endowment vector” that encapsulates their features and use game-theoretical methods to model the utility of link formation. After applying machine learning methods, we further analyze our model by examining micro- and macro- level properties of social networks as most agent-based models do. Our work contributes to the literature on network formation by combining the methods in game theory, agent-based modeling, machine learning, and computational sociology. Complex networks can be a useful tool to investigate problems in social science. Here the authors use game theory to establish a network model and then use a machine learning approach to characterize the role of nodes within a social network. Social networks are essential elements in societies, serving as channels for exchanging various benefits, such as innovation, information, and social support 5 – 8 . Moreover, research in social networks helps explain macro-level social phenomena, such as social polarization 9 and social contagion 10 , 11 . An understanding of social networks has significant implications, such as improving social welfare and political participation 12 , 13 . Previous work on modeling social network formation has typically employed game theory or agent-based modeling 14 – 20 . These studies typically propose simple and tractable micro-level rules for link formation mechanisms and show that these rules have implications for known macro-level properties. Several studies in statistics and econometrics have also used game theory to model empirical networks 21 – 23 , but they typically have been focused on estimating and identifying the effects of interest, such as racial segregation. To date, these models have not been capable of accounting for the effects of broad heterogeneity among individuals; therefore, they lack predictive power for link formation in complex, real-world networks. Each dimension in the latent space, therefore, typically does not correspond to a concrete attribute of the agents. The latent space representation of nodes on a network provides considerable potential for measuring heterogeneity among agents. However, because network embedding methods are designed for data representation and compression rather than for explaining network formation, they do not attempt to capture micro, inter-agent effects such as social status or macro effects such as social segregation; thus, they do not provide social science explanations for the link formation. Abstractly, we model link formation as a reaction-diffusion system, a framework found in many biological systems. Results A game theoretical model Endowment is a well-known and useful concept in microeconomic theory 32 , for example, fundamental theorems of welfare economics are based on agent exchanging endowments. In our model, an endowment vector could potentially represent all of the features (assets, abilities, capacities, qualities, etc.) that each agent possesses, and are treated as fixed, invariant characteristics of the agent. We do not consider the situation where endowments are dynamic in this study. In network game theory, pairwise stability 20 refers to the situation where no increased marginal utility can be brought to both agents of an unconnected pair, and no increased marginal utility can be brought to any agents who want to drop their neighbors. Following the definition, we derive the conditions when pairwise stability in undirected networks is satisfied. The proof is straightforward and can be found in Supplementary Note 1 . This result suggests that many characteristics that are described in the social science literature are due to the trade-off between coordination costs and exchange benefits, rather than being fundamental effects or biases. There are several interesting future directions based on this work. First, it is intriguing to consider the influence of existing neighbors on the marginal utilities of adding one more neighbor. For instance, the marginal utility of befriending a person should be higher when an ego has 10 friends than when the ego has 100 friends. Incorporating this interaction effect is difficult because this will require combinatorial optimization methods. We created a network of countries, where an edge indicates that the trade value between two countries is >1 billion dollars (for both directions). This process resulted in 100 countries with at least one link, and 703 undirected edges among them. We predict the GDP, economic complexity