The Convention Gap: Towards Measuring Implicit Communication in Cooperative AI Evaluation

Cooperative AI agents are evaluated against other AIs, yet human cooperation relies on implicit conventions---shared protocols for reading meaning beyond the literal message---which AI-AI benchmarks may not capture. We propose the \emph{convention gap}, the difference between the failure probability predicted from the literal content of communication and the observed failure rate, as a metric of implicit communication. In the card game Hanabi, the finite deck and deterministic hint constraints make this posterior exactly computable. We replayed about 101,000 play actions from three public datasets of human-human (hanab.live), AI-AI (HOAD), and human-AI (HanabiData) games. The gap was +26.2 percentage points (pp) in human pairs, $-$0.7~pp in AI pairs, and +16.4~pp in human-AI pairs, and was concentrated on plays of cards that had received no hints (+46~pp in human pairs). Within human-AI play, the literal information available to humans was similar across the three AI partners (mean predicted failure 38--41\%), but human failure rates ranged from 14.4\% to 34.4\% and the gap from +24.1 to +6.2~pp; the partner eliciting the largest gap produced the fewest human failures. Game score carried different information: it depended on each corpus's roster composition, whereas the gap separated human from AI play at the agent level. As a known-answer check, Off-Belief Learning agents, whose convention content is controlled by construction, gave a gap of +1.6~pp at the convention-free level, rising monotonically to +21.7~pp. These results suggest that convention compatibility, rather than AI-AI performance, may predict an AI's effectiveness with human partners.