Signaling Games

Game Theory · Axiom Academy

Unit 5: Games with Incomplete Information A signaling game has a specific sequential structure involving two players: The key feature is asymmetric information : the sender knows something the receiver doesn't, and the signal may reveal or conceal this information. 2. Informed Sender, Uninformed Receiver The sender knows their own type, which determines their preferences and payoffs. Common examples: The receiver forms beliefs about the sender's type based on the observed signal, then chooses an optimal response given those beliefs. 3. Costly Signals vs. Cheap Talk Not all signals are equally credible. The effectiveness of signaling depends critically on the cost structure: For a signal to be effective in equilibrium, it typically must be more costly for low types to mimic high types, creating a separating equilibrium . The typical sequence in a signaling game follows this pattern: Equilibrium analysis uses Perfect Bayesian Equilibrium, requiring consistent beliefs and optimal actions at every stage. 5. Education as Signaling: The Spence Model Michael Spence's job market signaling model is the canonical example of a signaling game: The key insight: Education can be valuable purely as a signal, even if it doesn't teach useful skills, because the cost of obtaining education is lower for high-ability workers. This creates a separating equilibrium where high types choose high education and low types choose low education.

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