Constructing a consistent shared spatial memory is a critical challenge in multi-agent systems, where partial observability and limited bandwidth often lead to catastrophic failures in coordination. We introduce a multi-agent predictive coding framework that formulates coordination as the minimization of mutual uncertainty among agents. Through an information bottleneck objective, this framework prompts agents to learn not only who and what to communicate but also when. At the foundation of this framework lies a grid-cell-like metric as internal spatial coding for self-localization, emerging spontaneously from self-supervised motion prediction. Building upon this internal spatial code, agents gradually develop a bandwidth-efficient communication mechanism and specialized neural populations that encode partners' locations-an artificial analogue of hippocampal social place cells (SPCs). These social representations are further utilized by a hierarchical reinforcement learning policy that actively explores to reduce joint uncertainty. On the Memory-Maze benchmark, our approach shows exceptional resilience to bandwidth constraints: success degrades gracefully from 73.5% to 64.4% as bandwidth shrinks from 128 to 4 bits/step, whereas a full-broadcast baseline collapses from 67.6% to 28.6%. Our findings establish a theoretically principled and biologically plausible basis for how complex social representations emerge from a unified predictive drive, leading to collective intelligence.