Evolve signaling systems and find pooling vs separating equilibria—see how communication emerges
Signaling games model situations where one player (the sender) has private information about their type and can send a costly signal to another player (the receiver), who then decides how to respond. The key question is: can honest communication emerge from strategic interaction?
A signaling game has three stages:
Different types send different signals, allowing the receiver to perfectly infer the sender's type. For example, high-ability workers get education while low-ability workers don't, and employers can distinguish them. This requires that signaling is less costly for high types (the single-crossing condition).
All types send the same signal, so the receiver learns nothing from the signal itself. The receiver must respond based only on their prior beliefs about the type distribution. For example, if no one gets education, employers can't distinguish worker types.
Some but not all types pool together. For instance, high types always signal, but low types signal with some probability, making the signal informative but not perfectly revealing.
For separating equilibria to exist, signaling must be less costly (or more beneficial) for high types than low types. This ensures high types have an incentive to signal while low types find it too expensive. Examples:
Michael Spence's seminal model showed how education could serve as a signal of worker ability even if it doesn't increase productivity. High-ability workers get education (costly signal) to distinguish themselves, and employers rationally pay them more. This creates a separating equilibrium where education reveals type.
The key insight is that signals must be costly to be credible. "Cheap talk" (costless messages) can't be trusted in settings with conflicting interests, because any type could claim to be high quality. Only costly signals that are harder to fake can credibly reveal private information.
Signaling games often have multiple equilibria, including implausible ones. Game theorists use equilibrium refinements like the Intuitive Criterion to rule out unreasonable equilibria by restricting receivers' off-equilibrium-path beliefs.
Biologist Amotz Zahavi proposed that costly traits like the peacock's elaborate tail serve as honest signals of genetic quality. Only healthy individuals can afford the cost of maintaining such handicaps, making them reliable indicators of fitness. This biological principle parallels economic signaling theory.
Signaling games extend the coordination problems seen in games like Coordination Games and Battle of the Sexes by adding asymmetric information. Like the Prisoner's Dilemma, they show how individual incentives can lead to socially suboptimal outcomes (e.g., excessive signaling costs without productivity gains).