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We investigate a prototypical agent-based model, the Naming Game, ontwo-dimensional random geometric networks. The Naming Game [A. Baronchelli etal., J. Stat. Mech.: Theory Exp. (2006) P06014.] is a minimal model, employinglocal communications that captures the emergence of shared communicationschemes (languages) in a population of autonomous semiotic agents. Implementingthe Naming Games with local broadcasts on random geometric graphs, serves as amodel for agreement dynamics in large-scale, autonomously operating wirelesssensor networks. Further, it captures essential features of the scalingproperties of the agreement process for spatially-embedded autonomous agents.Among the relevant observables capturing the temporal properties of theagreement process, we investigate the cluster-size distribution and thedistribution of the agreement times, both exhibiting dynamic scaling. We alsopresent results for the case when a small density of long-range communicationlinks are added on top of the random geometric graph, resulting in a"small-world"-like network and yielding a significantly reduced time to reachglobal agreement. We construct a finite-size scaling analysis for the agreementtimes in this case.

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