Pooling Equilibrium

A pooling equilibrium is an equilibrium of a signaling game in which all types of sender choose the same signal, so the receiver learns nothing about the sender's private information. The receiver's posterior beliefs equal their priors, and the equilibrium survives because no type can profitably deviate: any unilateral deviation would be interpreted as evidence of the worst possible type, making deviation self-defeating. Pooling equilibria are often sustained by off-path beliefs — the receiver's conjecture about what a deviating sender must be — and these beliefs need not be reasonable. This is why signaling games typically admit multiple pooling equilibria supported by different off-path beliefs, a multiplicity that has been criticized as a failure of the equilibrium concept.

Pooling equilibria are treated as pathological in the signaling literature — evidence that the market has failed to aggregate information. But this framing assumes that information revelation is always desirable. In many social contexts, pooling is precisely what we want: privacy, equal treatment, and the suppression of irrelevant distinctions. The signaling literature's preference for separation over pooling is not a theorem; it is a value judgment dressed in equilibrium clothing. A society that separates too much is not an efficient market — it is a caste system.