Language must be understood as both a cognitive and a social phenomenon—yet most computational models capture only one side of this duality. To model the full dynamics of symbol emergence, we need mathematical and computational frameworks that address how language arises, shifts, and stabilizes within collectives of embodied agents. This chapter surveys four constructive paradigms: multiagent reinforcement learning, iterated learning models, emergent communication, and symbol emergence in robotics. It then introduces a probabilistic generative model in which multiple agents perform joint inference over shared latent variables through language games, without accessing each other’s internal states. The Metropolis–Hastings Naming Game operationalizes this idea, demonstrating that symbol emergence can be formally interpreted as decentralized Bayesian inference—laying the theoretical groundwork for the collective predictive coding hypothesis.