Noise-Proof Equilibria in Two-Action Signaling Games
An equilibrium of a signaling game isnoise-proofif it survives a small perturbation of the Receiver's perception of the signal. We derive conditions for noise proofness and prove existence for signaling games where the Receiver has two actions, the message space is a real interval, and standard monotonicity conditions are met. Such games have a continuum of equilibria which satisfy the never-a-weak-best-reply criterion (NWBR), but often a unique noise-proof equilibrium. Every noise-proof equilibrium satisfies NWBR and is “insufficiently revealing”: With some probability the Receiver chooses an action which would be suboptimal under full information.