Scale-Free and Visibility Effects on Social and Economic Modeling

Abstract

This study investigates the influence of Barabási-Albert scale-free networks in shaping social dynamics, highlighting their role in driving two key phenomena: consensus evolution and price formation. In the first part, we extend the two-state majority-vote model by incorporating a visibility parameter V , which models a chance that an individual considers the opinion of a neighbor holding a differing stance in some social debate. This modification captures the asym- metric influence of agreement and dissent driven by algorithms in the so-called click economy, in which users are presented with content that agrees with their personal beliefs. Monte Carlo simulations reveal that the critical noise parameter qc increases with V , exhibiting an exuberant phase diagram characterized by both first-order and second-order phase transitions depending on the value of V and the network growth parameter z. In the second part, we analyze a three-state opinion dynamics model to investigate price formation in financial markets. Our model comprises two types of financial agents regarding their market strategies: noise traders and fundamentalists, whose financial options evolve via local or global influences, respectively. Numerical simulations show that the model reproduces key stylized facts of financial markets, including heavy-tailed return distributions, volatility clustering, and long-term memory of the volatility. An increase in the fraction of fundamentalist agents reflects a progressive loss of tails in the return distributions as they transition from a leptokurtic to a mesokurtic regime. Our results underscore the crucial impact of scale-free networks in driving emergent behaviors in socioeconomic modeling, providing an extensive framework for complex systems investigation.