Cheap Talk

Game Theory · Axiom Academy

Unit 5 - Games with Incomplete Information Cheap talk refers to communication that is: Costless : The sender pays no cost to send any particular message Non-binding : Messages create no enforceable commitments Payoff-irrelevant : The message itself doesn't directly affect payoffs Examples include pre-game announcements, casual conversation, and informal advice. The key question: when should a rational receiver believe such messages? 2. When is Cheap Talk Credible? For cheap talk to be informative in equilibrium, there must be sufficient alignment of interests between sender and receiver. Key Insight: If the sender and receiver have completely opposed preferences, cheap talk cannot convey information - any message would be dismissed as manipulation. However, with partial alignment of interests, informative equilibria can exist where: The sender truthfully reveals some information The receiver acts on this information Both players are better off than with no communication Crawford and Sobel (1982) analyzed a canonical cheap talk game: Sender observes a state θ (e.g., product quality, expert knowledge) Sender sends a costless message m to the receiver Receiver takes action a based on the message Preferences : Both prefer actions closer to the state, but sender has a bias b The model shows that perfect information transmission is impossible with bias, but partial information transmission can occur through interval partitions.

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