Persistent agents in Axelrod's social dynamics model

Abstract

Axelrod's model of social dynamics has been studied under the effect of external media. Here we study the formation of cultural domains in the model by introducing persistent agents. These are agents whose cultural traits are not allowed to change but may be spread through local neighborhood. In the absence of persistent agents, the system is known to present a transition from a monocultural to a multicultural regime at some critical Q (number of traits). Our results reveal a dependence of critical Q on the occupation probability p of persistent agents and we obtain the phase diagram of the model in the (p, Q)-plane. The critical locus is explained by the competition of two opposite forces named here barrier and bonding effects. Such forces are verified to be caused by non-persistent agents which adhere (adherent agents) to the set of traits of persistent ones. The adherence (concentration of adherent agents) as a function of p is found to decay for constant Q. Furthermore, adherence as a function of Q is found to decay as a power law with constant p.

Effect of long-range interactions on the phase transition of Axelrod's model

“…Axelrod's model exhibits a good balance between simplicity and realism, being considered a choice model to study collective social phenomena from a quantitative perspective [30]. For instance, Axelrod's model has proven useful to study the effects of global media on the polarization of public opinion [31][32][33][34] as well as to understand the emergence of a collective intelligence from the local interactions between dumb agents [35,36]. However, rather than explore the riveting applications of Axelrod's model in social and political science [4], here we focused on the not less enthralling contributions of Axelrod's model to statistical physics [2].…”

Another phase transition in the Axelrod model

“…Other extensions and variations of the Axelrod model include bounded confidence and metric features [23], agent migration [34,[47][48][49], extended conservativeness (a preference for the last source of cultural information) [50], surface tension [51], cultural repulsion [52], the presence of some agents with constant culture vectors [53,54], having one or more features constant on some [55] or all [49] agents, using empirical [56,57] or simulated [57,58] rather than uniform random initial culture vectors, comparing mass media model predictions to empirical data on a mass media campaign [11], coupling two Axelrod models through global fields [59,60], combining the Axelrod model with a spatial public goods game [26], modeling diffusion of innovations by adding a new trait on a feature [61], and even using it as a heuristic for an optimization problem [62].…”

“…In addition to the earliest phase diagrams showing just q and the order parameter [5] or the noise rate r and the order parameter [19,24], the following phase diagrams, derived from either simulation experiments, or mean-field analysis (or both), have been drawn for the Axelrod model and various extensions (notation may be changed from the original papers for consistency): q -B where B is external field strength [8,9,11,15,30]; r -ν and B -ν where r is noise rate, and ν is a parameter controlling the network clustering structure [10]; q -o where o is the degree of overlap between the layers of a multilayer network [25]; θ -q where θ is the "bounded confidence" threshold (minimum cultural similarity required for interaction) [23]; F -q for the one-dimensional case [36]; κ -q where κ is the fraction of "persistent agents" or "opinion leaders" (those with a constant culture vector) [53,54].…”