A closer look at two conjectures about irregular marginal revenue

Abstract

A common assumption in models where buyers have private information is for the buyers to draw their private values from distribution F with density f. Optimal mechanisms differ depending on whether the marginal revenue (buyer’s virtual valuation) is increasing (in which case F is said to be regular) or not increasing (in which case F is said to be irregular). This note examines two conjectures about sufficient conditions for irregularity made in the literature—made but not proven. We develop counterexamples to show that these conjectures are false, thereby reducing the set of distributions previously thought to be irregular.