  We study market interactions in which buyers are allowed to credibly reveal
partial information about their types to the seller. Previous recent work has
studied the special case of one buyer and one good, showing that such
communication can simultaneously improve social welfare and ex ante buyer
utility. However, with multiple buyers, we find that the buyer-optimal
signalling schemes from the one-buyer case are actually harmful to buyer
welfare. Moreover, we prove several impossibility results showing that, with
either multiple i.i.d. buyers or multiple i.i.d. goods, maximizing buyer
utility can be at odds with social efficiency, which is surprising in contrast
with the one-buyer, one-good case. Finally, we investigate the computational
tractability of implementing desirable equilibrium outcomes. We find that, even
with one buyer and one good, optimizing buyer utility is generally NP-hard but
tractable in a practical restricted setting.
