Naming Games in Two-Dimensional and Small-World-Connected Random Geometric Networks

TL;DR

This paper studies the Naming Game, an agent-based model for language emergence, on 2D and small-world random geometric networks, revealing how network structure influences agreement dynamics and scaling properties.

Contribution

It introduces the Naming Game on random geometric graphs with local broadcasts and analyzes how small-world links accelerate agreement in spatially-embedded networks.

Findings

Agreement times exhibit dynamic scaling.

Small-world links significantly reduce convergence time.

Cluster-size distribution follows scaling laws.

Abstract

We investigate a prototypical agent-based model, the Naming Game, on two-dimensional random geometric networks. The Naming Game [A. Baronchelli et al., J. Stat. Mech.: Theory Exp. (2006) P06014.] is a minimal model, employing local communications that captures the emergence of shared communication schemes (languages) in a population of autonomous semiotic agents. Implementing the Naming Games with local broadcasts on random geometric graphs, serves as a model for agreement dynamics in large-scale, autonomously operating wireless sensor networks. Further, it captures essential features of the scaling properties of the agreement process for spatially-embedded autonomous agents. Among the relevant observables capturing the temporal properties of the agreement process, we investigate the cluster-size distribution and the distribution of the agreement times, both exhibiting dynamic scaling. We also present results for the case when a small density of long-range communication links are added on top of the random geometric graph, resulting in a "small-world"-like network and yielding a significantly reduced time to reach global agreement. We construct a finite-size scaling analysis for the agreement times in this case.