Monotone equilibria in signaling games

We examine the monotonicity of the sender's equilibrium strategy with respect to her type in signaling games. We show that when the sender's return from the receiver's action depends on her type, the Spence–Mirrlees condition cannot rule out equilibria in which a higher-type sender chooses a strictly lower action than a lower-type. We provide sufficient conditions under which all equilibria are monotone, which require that the sender's payoff is decreasing in her action, is increasing in the receiver's action, and has strictly increasing differences between her type and the action profile. We apply our sufficient conditions to education signaling, advertising, and warranty provision.