Homonyms and context in signalling game with reinforcement learning

Using multi-agent signalling game with reinforcement learning, we examine the influence of context on the dynamics of homonyms. In our approach, context denotes additional information sent to the receiver, which helps to recognise the signal. Agents in our model select a communicated word or its interpretation with a probability proportional to the power of its weight, which accumulates over previous successful communication attempts (probability~weightα). The behaviour of the model hinges to some extent on whether this probability depends linearly ([Formula: see text]) or superlinearly ([Formula: see text]) on the weight. Numerical as well as analytical results show that contextuality stabilizes homonyms and also affects the overall dynamics of language formation. While in the linear regime, contextuality can hinder the formation of an efficient language, in the superlinear regime-it can even speed up the process. Some aspects of the evolution of homonyms in our model can be understood using a certain urn model. Mathematical analysis demonstrates that in the superlinear regime and in the presence of contextuality, the urn model predicts the existence of polarised-like homonyms, while in the linear regime, only symmetric homonyms can exist. Since there are polarised homonyms in natural languages, our work suggests that the superlinear regime (which could be considered as a manifestation of the so-called Metcalfe's law) may be more appropriate to describe language formation than the linear regime.