In the studies on symbol emergence and emergent communication in a population of agents, a computational model was employed in which agents participate in various language games. Among these, the Metropolis-Hastings naming game (MHNG) possesses a notable mathematical property: symbol emergence through MHNG is proven to be a decentralized Bayesian inference of representations shared by the agents. However, the previously proposed MHNG is limited to a two-agent scenario. This paper extends MHNG to an N-agent scenario. The main contributions of this paper are twofold: (1) we propose the recursive Metropolis-Hastings naming game (RMHNG) as an N-agent version of MHNG and demonstrate that RMHNG is an approximate Bayesian inference method for the posterior distribution over a latent variable shared by agents, similar to MHNG; and (2) we empirically evaluate the performance of RMHNG on synthetic and real image data, enabling multiple agents to develop and share a symbol system. Furthermore, we introduce two types of approximations -- one-sample and limited-length -- to reduce computational complexity while maintaining the ability to explain communication in a population of agents. The experimental findings showcased the efficacy of RMHNG as a decentralized Bayesian inference for approximating the posterior distribution concerning latent variables, which are jointly shared among agents, akin to MHNG. Moreover, the utilization of RMHNG elucidated the agents' capacity to exchange symbols. Furthermore, the study discovered that even the computationally simplified version of RMHNG could enable symbols to emerge among the agents.

翻译：在关于智能体群体中符号涌现与涌现式通信的研究中，常采用参与者进行多种语言博弈的计算模型。其中，Metropolis-Hastings命名博弈（MHNG）具有显著的数学性质：通过MHNG实现的符号涌现被证明是智能体共享表征的分布式贝叶斯推理。然而，此前提出的MHNG仅局限于双智能体场景。本文将MHNG扩展至N智能体场景。本文的主要贡献有二：（1）提出递归式Metropolis-Hastings命名博弈（RMHNG）作为MHNG的N智能体版本，并证明RMHNG与MHNG类似，是对智能体间共享潜变量后验分布的近似贝叶斯推理方法；（2）在合成图像和真实图像数据上对RMHNG进行实证评估，使多个智能体能够发展并共享符号系统。此外，我们引入两种近似方法（单样本近似和有限长度近似）以降低计算复杂度，同时保持对智能体群体中通信行为的解释能力。实验结果表明，RMHNG与MHNG类似，能有效作为近似智能体间共同共享潜变量后验分布的分布式贝叶斯推理方法。同时，RMHNG的使用揭示了智能体交换符号的能力。研究进一步发现，即使采用计算简化版本的RMHNG，也能使符号在智能体间涌现。