Modelling the expectations of economic agents with networks - The dynamics of agreement

Abstract

In this paper, I examine how different network relationship structures influence the expectations of economic agents. For each agent, its credibility is known (trust index), i.e. the weight that its opinion should be given by other actors when forming their own opinions. The analysis focuses on the dynamics of consensus formation under different initial distributions (uniform, normal, beta) for both the trust index and the initial expectations. Using directed networks generated by the Barabási-Albert and Erdős-Rényi models, I simulate interactions among agents, testing nine combinations of trust index and initial expectation distributions. Scale-free networks are chosen for their ability to represent hubs of high influence, which are common in economic systems, while Erdős–Rényi networks provide a baseline for randomness. The results show that dense networks, such as Erdős-Rényi random networks with high threshold probabilities, consistently reach consensus faster than sparse or scale-free networks. Uniform and normal distributions of trust indices and initial expectations facilitate faster alignment, whereas beta distributions introduce variability and slower convergence. These findings illustrate how the critical role of network density and individual heterogeneity in shaping consensus dynamics, using a simulation model to offer valuable insights into the interplay between structure and behaviour in networked systems.