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Analyzing Social Behavior with Game Theory

Article: https://www.nature.com/articles/s41467-019-13148-8

Title: Game Theoretical Inference of Human Behavior in Social Networks

In class, we have learned about the utility of Nash equilibriums in predicting game outcomes while analyzing what each actor stands to gain from different actions. We have also learned about power laws, which are related to the concept of preferential attachment (aka rich get richer)- the idea that newborn nodes are more likely to link to nodes which already have a lot of links.

The article connects multiple concepts we’ve learned in class, while also touching on adjacent areas that we did not cover. There were a couple of key parts that I found most interesting.

First of all, the article discusses preferential attachment, which was mostly referred to as the “rich-get-richer” throughout this course. The course text discusses how  “the goal is not to capture all the reasons why people create links on the Web, or in any other network, but to show that a simple and very natural principle behind link creation leads directly to power laws.” Most of the examples we dealt with involved fairly simple problems, and we did not have to worry about the reasoning behind why one page might link to another aside from analyzing existing links according to the rich-get-richer rule. Furthermore, we generally had each node only form one link, which greatly simplified the math and theory involved. The article goes much more in depth, discussing micro-scale, sociological reasons why pages might choose to link a certain way, and also analyzing much more complex networks with more nodes and more links. It states a widely supported theory that “actors strategically choose their relations to optimize their network positions in an incentive-guided fashion,” going beyond simply choosing based on popularity, and generally aiming for centrality, or importance. The specific aims of actors can have a large effect on the structure and stability of the network formed. For example, “when actors strive for betweenness centrality, balanced complete bipartite (or more generally multipartite) networks are stable.” There is much opportunity for mathematical and theoretical analysis of these properties, and the paper goes greatly into depth.

The researchers employed a complex Nash equilibrium condition to statistically predict behavior of actors, even taking into account that not all actors will necessarily act rationally, and furthermore defined a payoff function which was “a parametric combination of different incentives: influence, brokerage, closure.” They analyzed several scenarios, including one where they focused on eight newborn nodes. In a smaller network, these nodes tended to form clusters through reciprocal links, but as the network got larger, these tendencies largely faded.

Overall, it was fascinating to read a paper with models that were less simplified to see how the theories we learn in this course can be combined and applied to complex, real-world situations.

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