How a group that cannot communicate knows itself by its enemy

Abstract

Teams that cannot communicate seem stuck with what each member sees. We show that their opponent can tell them the rest. Silent hunters, jammed robots and traders who never meet all face an adversary that reacts to the group as a whole; every member can read that reaction, a tell, and learn what no member knows alone. One tell can do the work of a message from every member. The adversary would rather hide, but hiding interferes with its own task, and a team that commits in advance to how it will respond decides how much hiding is worth. A committed team never loses when its opponent cares more about its own goals, and does as well as a fully informed team exactly when the opponent's stake outweighs any gain from lying. Below that point the team learns more by trusting less: in a solved Gaussian model it obtains the truth by promising not to use all of it and keeps the cost the opponent would have paid to conceal; an exact test decides when this holds in finite games. How a team spreads its trust matters too. A lone uninformed member with a full-support prior needs a private coin, but with additive squared-error losses two interchangeable members who respond differently replace it, and a small discount on trust insures against misjudging the enemy. Information, on this view, is not only gathered or aggregated; it is produced by how a team commits to respond.