Analysis of naming game over networks in the presence of memory loss

In this paper, we study the dynamics of naming game where individuals are under the influence of memory loss. An extended naming game incorporating memory loss is proposed. Different from the existing naming game models, the individual in the proposed model would forget some words with a probability in his memory during interaction and keep his conveyed word unchanged until he reaches a local agreement. We analyze the dynamics of the proposed model through extensive and comprehensive simulations, where four typical networks with different configuration are employed. The influence of memory loss as well as the population size on the performance of the proposed model is investigated. The simulation results show that (i) the stronger memory loss, the larger convergence time; (ii) as the strength of memory loss becomes stronger, maximum number of total words will decrease, while the maximum number of different words among the population remains almost unchanged; (iii) the maximum number of different words increases linearly with the increase of the population size and coincides with each other under different strength of memory loss. The findings in the proposed model may give an insight to understand better the influence of memory loss on the transient dynamics of language evolution and opinion formation over networks.