In game theory, cheap talk is communication between players that does not directly affect the payoffs of the game. Providing and receiving information is free. This is in contrast to signaling in which sending certain messages may be costly for the sender depending on the state of the world.
This basic setting set by Vincent Crawford and Joel Sobel has given rise to a variety of variants.
To give a formal definition, cheap talk is communication that is: costless to transmit and receive non-binding (i.e. does not limit strategic choices by either party) unverifiable (i.e. cannot be verified by a third party like a court) Therefore, an agent engaging in cheap talk could lie with impunity, but may choose in equilibrium not to do so.
Applications
Game theory
Cheap talk can, in general, be added to any game and has the potential to enhance the set of possible equilibrium outcomes. For example, one can add a round of cheap talk in the beginning of the Battle of the Sexes. Each player announces whether they intend to go to the football game, or the opera. Because the Battle of the Sexes is a coordination game, this initial round of communication may enable the players to select among multiple equilibria, thereby achieving higher payoffs than in the uncoordinated case. The messages and strategies which yield this outcome are symmetric for each player. They are: 1) announce opera or football with even probability 2) if a person announces opera (or football), then upon hearing this message the other person will say opera (or football) as well (Farrell and Rabin, 1996). If they both announce different options, then no coordination is achieved. In the case of only one player messaging, this could also give that player a first-mover advantage.
It is not guaranteed, however, that cheap talk will have an effect on equilibrium payoffs. Another game, the Prisoner's Dilemma, is a game whose only equilibrium is in dominant strategies. Any pre-play cheap talk will be ignored and players will play their dominant strategies (Defect, Defect) regardless of the messages sent.
Biological applications
It has been commonly argued that cheap talk will have no effect on the underlying structure of the game. In biology authors have often argued that costly signalling best explains signalling between animals (see Handicap principle, Signalling theory). This general belief has been receiving some challenges (see work by Carl Bergstrom and Brian Skyrms 2002, 2004). In particular, several models using evolutionary game theory indicate that cheap talk can have effects on the evolutionary dynamics of particular games.
Crawford and Sobel's definition
Setting
In the basic form of the game, there are two players communicating, one sender S and one receiver R.
Type
Sender S gets knowledge of the state of the world or of his "type" t. Receiver R does not know t ; he has only ex-ante beliefs about it, and relies on a message from S to possibly improve the accuracy of his beliefs.
Message
S decides to send message m. Message m may disclose full information, but it may also give limited, blurred information: it will typically say "The state of the world is between t1 and t2". It may give no information at all.
The form of the message does not matter, as long as there is mutual understanding, common interpretation. It could be a general statement from a central bank's chairman, a political speech in any language, etc. Whatever the form, it is eventually taken to mean "The state of the world is between t1 and t2".
Action
Receiver R receives message m. R updates his beliefs about the state of the world given new information that he might get, using Bayes's rule. R decides to take action a. This action impacts both his own utility and the sender's utility.
Utility
The decision of S regarding the content of m is based on maximizing his utility, given what he expects R to do. Utility is a way to quantify satisfaction or wishes. It can be financial profits, or non-financial satisfaction—for instance the extent to which the environment is protected. → Quadratic utilities: The respective utilities of S and R can be specified by the following: