Naming Games in Two-Dimensional and Small-World-Connected Random Geometric Networks
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.
Keywords
Cite
@article{arxiv.1103.5269,
title = {Naming Games in Two-Dimensional and Small-World-Connected Random Geometric Networks},
author = {Qiming Lu and G. Korniss and B. K. Szymanski},
journal= {arXiv preprint arXiv:1103.5269},
year = {2011}
}