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In multi-agent collaboration problems with communication, an agent's ability to encode their intention and interpret other agents' strategies is critical for planning their future actions. This paper introduces a novel algorithm called Intention Embedded Communication (IEC) to mimic an agent's language learning ability. IEC contains a perception module for decoding other agents' intentions in response to their past actions. It also includes a language generation module for learning implicit grammar during communication with two or more agents. Such grammar, by construction, should be compact for efficient communication. Both modules undergo conjoint evolution - similar to an infant's babbling that enables it to learn a language of choice by trial and error. We utilised three multi-agent environments, namely predator/prey, traffic junction and level-based foraging and illustrate that such a co-evolution enables us to learn much quicker (50%) than state-of-the-art algorithms like MADDPG. Ablation studies further show that disabling the inferring belief module, communication module, and the hidden states reduces the model performance by 38%, 60% and 30%, respectively. Hence, we suggest that modelling other agents' behaviour accelerates another agent to learn grammar and develop a language to communicate efficiently. We evaluate our method on a set of cooperative scenarios and show its superior performance to other multi-agent baselines. We also demonstrate that it is essential for agents to reason about others' states and learn this ability by continuous communication.