Topology-induced coarsening in language games

Area of Science:

• Complex Systems
• Computational Social Science
• Statistical Physics

Background:

• Investigating emergent global consensus from local interaction rules is crucial for understanding collective behavior.
• Semiotic dynamics, particularly the naming game model, provides a framework for studying how agents establish shared conventions.
• Understanding the impact of spatial structure on consensus formation is key to bridging microscopic rules and macroscopic outcomes.

Purpose of the Study:

• To compare consensus convergence mechanisms in the naming game model between low-dimensional lattices and mean-field approximations.
• To analyze the cognitive effort, memory requirements, and time scales associated with consensus formation in different spatial dimensions.
• To provide analytical and numerical evidence for the scaling behavior of convergence in various dimensions.

Main Methods:

• Agent-based modeling of the naming game on low-dimensional lattices (d <= 4) and comparison with mean-field analysis.
• Mapping the one-dimensional boundary dynamics to a truncated Markov process for analytical computation of the diffusion coefficient.
• Analytical derivation and numerical simulation of memory and time scaling for consensus convergence as a function of population size (N) and dimension (d).

Main Results:

• Low-dimensional lattices facilitate consensus through a coarsening process, demanding less cognitive effort per agent compared to mean-field.
• Consensus formation takes longer in low dimensions, with convergence time scaling as N^(1+2/d) up to the upper critical dimension (d=4).
• In contrast, mean-field models exhibit memory and time scaling of N^(3/2).

Conclusions:

• Spatial structure significantly influences the efficiency and dynamics of consensus formation in large populations.
• The trade-off between cognitive effort and convergence time highlights the importance of dimensionality in collective learning and agreement.
• The findings offer insights into the emergence of shared meaning and coordination in decentralized systems.