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Cheap talk


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.

One actor has information and the other has ability to act. The informed player can choose strategically what to say and what not to say. Things become interesting when the interests of the players are not aligned. The classic example is of an expert (say, an ecologist) trying to explain the state of the world to an uninformed decision maker (say, politician voting on a deforestation bill). The decision maker, after hearing the report from the expert, must then make a decision which affects the payoffs of both players.

This basic setting set by Crawford and Sobel has given rise to a variety of variants.

To give a formal definition, cheap talk is communication that is:

Therefore an agent engaging in cheap talk could lie with impunity, but may choose in equilibrium not to do so.

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:


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