Can Buyers Reveal for a Better Deal?

We study small-scale 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 where there is one buyer and one good, showing that such communication can simultaneously improve social welfare and ex ante buyer utility. 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 a surprising contrast to 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.