Signaling with Costly Acquisition of Signals

In this paper we identify a novel reason why signaling may fail to separate types, which
is specific to cases where the receiver has to incur a cost to acquire the signal sent by the
sender. If the receiver chooses not to incur the acquisition cost, then all sender’s types
find it optimal to pool on the least costly signal; also, if all sender’s types pool on the
least costly signal, then the receiver finds it optimal not to incur the acquisition cost.
This kind of coordination failure makes the resulting pooling equilibrium extremely
robust, even when costs of signal acquisition are very small. Also, pooling is shown to
be robust to all refinements based on out-of-equilibrium beliefs, even when the sender
can engage in further signaling that can act as an “invitation” to acquire the main
signal, and when acquisition costs are smooth and depend on the receiver’s effort to
acquire the signal. These results provide a new source of interest in pooling equilibria