Signaling Under Double-Crossing Preferences

This paper provides a general analysis of signaling under double-crossing preferences with a continuum of types. There are natural economic environments where the indifference curves of two types cross twice, such that the celebrated single-crossing property fails to hold. Equilibrium exhibits a threshold type below which types choose actions that are fully revealing and above which they pool in a pairwise fashion, with a gap separating the actions chosen by these two sets of types. The resulting signaling action is quasi-concave in type. We also provide an algorithm to establish equilibrium existence by construction.