Algorithmic Cheap Talk.

The literature on strategic communication originated with the influential cheap talk model, which precedes the Bayesian persuasion model by three decades. This model describes an interaction between two agents: sender and receiver. The sender knows some state of the world which the receiver does not know, and tries to influence the receiver's action by communicating a cheap talk message to the receiver. This paper initiates the algorithmic study of cheap talk in a finite environment (i.e., a finite number of states and receiver's possible actions). We first prove that approximating the sender-optimal or the welfare-maximizing cheap talk equilibrium up to a certain additive constant or multiplicative factor is NP-hard. Fortunately, we identify three naturally-restricted cases that admit efficient algorithms for finding a sender-optimal equilibrium. These include a state-independent sender's utility structure, a constant number of states or a receiver having only two actions.