Small Noise in Signaling Selects Pooling on Minimum Signal

In this paper we study how the presence of a small amount of noise in signaling games
impacts on the likelihood of separation and, hence, the likelihood of information transmission. We consider a variant of a standard signaling model where a source of exogenous noise affects the signals that agents observe. Noise, even if tiny, poses tight
constraints on beliefs by making all signals possible along the equilibrium path. We
show that separation cannot be obtained in equilibrium if the noise is small enough
– but not nil. In particular, for any separating profile, if noise is sufficiently small
then the sender has a profitable deviation consisting of a signal reduction. Instead, the
pooling equilibrium where all sender’s types pool on the minimum signal always exists,
independently of the level of noise. These results provide a new source of interest in
pooling equilibria.