Naming game with learning errors in communications

TL;DR

This paper introduces a model of the naming game incorporating communication errors, analyzing how errors influence consensus, memory requirements, and convergence across different network topologies, with strategies to mitigate errors.

Contribution

It proposes the NGLE model with strategies to prevent learning errors and studies their effects on convergence and memory in various network structures.

Findings

Learning errors slightly slow convergence.

Errors increase memory requirements linearly.

A threshold error rate impairs convergence.

Abstract

Naming game simulates the process of naming an objective by a population of agents organized in a certain communication network topology. By pair-wise iterative interactions, the population reaches a consensus state asymptotically. In this paper, we study naming game with communication errors during pair-wise conversations, where errors are represented by error rates in a uniform probability distribution. First, a model of naming game with learning errors in communications (NGLE) is proposed. Then, a strategy for agents to prevent learning errors is suggested. To that end, three typical topologies of communication networks, namely random-graph, small-world and scale-free networks with different parameters, are employed to investigate the effects of various learning errors. Simulation results on these models show that 1) learning errors slightly affect the convergence speed but distinctively increase the requirement for memory of each agent during lexicon propagation; 2) the maximum number of different words held by the whole population increases linearly as the value of the error rate increases; 3) without applying any strategy to eliminate learning errors, there is a threshold value of the learning errors which impairs the convergence. The new findings help to better understand the role of learning errors in naming game as well as human language development from a network science perspective.