Ironing in TU dynamic auctions when virtual values are nonmonotone

Establish whether an ironing procedure in the sense of Myerson (1981) is required and how it should be constructed in the TU dynamic auction model when the virtual value function J(v)=v−(1−2α)(1−F(v))/f(v) fails to be monotone (e.g., for α>1/2 when the inverse hazard rate decreases too rapidly), and characterize the resulting optimal mechanism under such non-regular cases.

Background

The TU model extends classic Myerson-style mechanism design to a dynamic environment with stochastic arrivals of buyers and goods. The analysis assumes the virtual value J(v) is nondecreasing to apply standard arguments.

The authors note that this regularity holds under certain distributions and parameter ranges. When it fails—for instance, if the inverse hazard rate decreases too quickly for α>1/2—they explicitly conjecture that an ironing procedure akin to Myerson’s static approach would apply, leaving the precise dynamic ironing construction and resulting optimal mechanism open.