Incorporating Game Theory and Nash Equilibrium Concepts to Predict Social Network Community Behaviors

In June 2016, there were an estimated 1.55 billion active users on the most popular social media platform, Facebook[1]. As of April 26th, 2017, there were an estimated 700 million active users on Instagram, our main social media platform for this research. As the number of users on social media platforms increases, a problem of great significance becomes clear: the increasing amount of negativity within the communities. Our goal in this paper is to use the concepts of game theory and Nash Equilibrium to solve this problem. We create a game that has two social media users, or players, trying to extend their outreach while keeping a positive community. Using five variables collected from various Instagram profiles, we create cost and payoff functions for the decision making part of game theory. We implement those functions and make several discoveries: contrary to popular belief, the comments and negative comment percentage are not correlated; the number of followers directly affects the number of likes on a user’s posts; the cost function output increases with the payoff function output in a strong positive correlation; and that a follower number increase on an account will almost always result in an increase in number of comments. Future work could explore implementing our functions with the Gambit library for game theory and incorporating the mathematical portion of Nash Equilibrium into our solution.