Opinion Dynamics for Utility Maximizing Agents with Heterogeneous Resources

In this paper we propose a continuous-time non-linear model of opinion dynamics. One of the main novelties of our model is that it costs resources for an agent to express an opinion. Each agent receives a utility based on the complete opinion profile of all agents. Each agent seeks to maximize its own utility function by suitably revising its opinion and the proposed dynamics arises from all agents simultaneously doing this. For the proposed model, we show ultimate boundedness of opinions. We also show stability of equilibrium points and convergence to an equilibrium point when all agents are non-contrarian. We give conditions for the existence of a consensus equilibrium and analyze the role that resources play in determining the social power of the agents in terms of the deviation of the consensus value from the agents’ internal preference. We also carry out a Nash equilibrium analysis of the underlying game and show that when all agents are non-contrarian, the set of equilibria of the opinion dynamics is the same as the set of Nash equilibria for the underlying game. We illustrate our results using simulations.