Coordination Games with Sequential Stochastic Learning and Language Emergence

Lewis signaling game (LSG) and similar coordination games have been used to model the emergence and evolution of language. However both Nash equilibria and learning or evolutionary dynamics often result in suboptimal signaling systems. We present a sequential reinforcement learning (SRL) model based on a novel sequential binary decision process. SRL has low cognitive demands and parameter count and exhibits lateral inhibition without additional assumptions. We prove all scenarios converge to an optimal signaling system in all N state, N signal LSGs with arbitrary state probabilities and further explore its properties with numerical simulations. Next, we model a signaling game with agents who both speak and hear while using one state of learning (instead of two, as is common). Agents have a probability distribution for meanings in a given context. Speaking agents use the distribution to choose a meaning and use SRL model to choose a signal. Hearing agents use Bayes to combine their state of learning with their meaning distribution to guess a meaning. An agent's state of learning is reinforced from habit of speaking and guessing a meaning. Numerical simulations indicate both agents converge to the same optimal system without external reinforcement as happens in language acquisition.