Polarization Game over Social Networks

This paper quantitatively analyzes a game over a social network of agents (nodes), some of which are controlled by two players who maximize and minimize polarization over this network. Agents' opinions evolve according to the Friedkin-Johnsen model, and players can change only the innate opinion of an agent. Polarization is measured as the sample variance of the agents' steady-state opinions. The game is considered void if the players choose the same agents, which constitutes a zero-sum game. We first analyze the functional properties of this game and characterize the best response for each player given the agent. Fictitious play is used to obtain the equilibria in real social networks. Subsequently, the paper delves into an exploration of the properties of the Nash equilibrium (NE).