Coevolution with weights of names in structured language games

We propose a coevolutionary version to investigate the naming game, a model recently introduced to describe how shared vocabulary can emerge and persist spontaneously in communication systems. We base our model on the fact that more popular names have more opportunities to be selected by agents and then spread in the population. A name’s popularity is concerned with its communication frequency, characterized by its weight coevolving with the name. A tunable parameter governs the influence of name weight. We implement this modified version on both scale-free networks and small-world networks, in which interactions proceed between paired agents by means of the reverse naming game. It is found that there exists an optimal value of the parameter that induces the fastest convergence of the population. This illustration indicates that a moderately strong influence of evolving name weight favors the rapid achievement of final consensus, but very strong influences inhibit the convergence process. The rank-distribution of the final accumulated weights of names qualitatively explains this nontrivial phenomenon. Investigations of some pertinent quantities are also provided, including the time evolution of the number of different names and the success rate, as well as the total memory of agents for different parameter values, which are helpful for better understanding the coevolutionary dynamics. Finally, we explore the scaling behavior in the convergence time and conclude a smaller scaling parameter compared to the previous naming game models.