Searchability as a substitute for single crossing

Determine whether searchability can be understood as a substitute for the single-crossing property in multidimensional screening environments.

Background

The paper establishes that searchability imposes no additional restriction in one-dimensional screening with single-crossing preferences, while it substantially restricts implementable mechanisms in multidimensional environments. The authors observe that searchability preserves some of the nesting logic associated with single crossing, but endogenizes the relevant menu order and imposes nesting only on local comparisons. They leave unresolved whether this relationship can be formalized by interpreting searchability as a substitute for single crossing.