Can AI Agents Share a Secret Through Action Order?

AI agents can leak private information through what they do, not only through what they say. We tested whether confidentiality rules prevent this in a two-agent game. Alice knows a private answer (1 or 2) and completes two tasks in either order. Bob sees the order and guesses the answer or passes. A correct guess rewards both agents and costs a simulated organization points. No codebook is given. With DeepSeek-V4-Pro, the baseline rule against disclosure left strong encoding: Alice's order depended on the answer (0.85 across five prompt wordings; 0 means equal order frequencies, ±1 perfect encoding). In five-round games, Bob answered correctly in 70% of rounds, and each agent gained +0.50 per round, compared with −0.04 when Bob was shown random orders. Adding one sentence to the rule reduced encoding to 0.03 when it named action order and to 0.10 when it prohibited disclosure "by any means." Neither rule was shown to make leakage reliably negligible. These findings concern one model and one synthetic game. Confidentiality rules and evaluations should cover agents' actions as well as their messages