Cheap Talking Algorithms

Consider the classic signalling game: a sender is informed about a payoff-relevant state of the world drawn from a known distribution and takes one of several possible actions; an uninformed receiver observes the action but not the state, and makes a decision. In a landmark paper, Crawford and Sobel (1982) (henceforth CS) showed that, even if the payoff of both agents is independent of the sender's action, there are equilibria where the action transmits information about the state, as long as the conflict of interest between the agents about the ideal receiver's decision is not too large. By interpreting the payoff-irrelevant actions of the sender as "cheap talk", CS delivers a powerful formal theory of communication. Non-committal and purely symbolic behaviour can convey information and help coordinate subsequent interactions even if rational agents do not share identical goals. In this paper, we compute stationary points of independent reinforcement learning algorithms playing the CS's game of information transmission.