People coordinate without communication by converging on mutually obvious signals [definitional]
When a man loses his wife in a department store without any prior understanding on where to meet if they get separated, the chances are good that they will find each other. It is likely that each will think of some obvious place to meet, so obvious that each will be sure that the other is sure that it is “obvious” to both of them. One does not simply predict where the other will go, since the other will go where he predicts the first to go, which is wherever the first predicts the second to predict the first to go, and so ad infinitum. Not “What would I do if I were she?” but “What would I do if I were she wondering what she would do if she were I wondering what I would do if I were she. ..?” What is necessary is to coordinate predictions, to read the same message in the common situation, to identify the one course of action that their expectations of each other can converge on. They must “mutually recognize” some unique signal that coordinates their expectations of each other.
XREF: Recalls Thomas Schelling's focal point theory in game theory.
Thomas C. Schelling, The Strategy of Conflict, loc. 134