Resolve overlapping revenue bounds under smooth beliefs

Determine the revenue ranking between exactly truthful, no-subsidy band mechanisms on a fixed partition and conventional auction formats, including first-price and second-price auctions, under the smooth atomless belief model in cases where the available feasible-revenue and upper-bound intervals overlap.

Background

The paper compares finite-band payment mechanisms with conventional auctions under a common smooth, atomless belief environment. For some band partitions and belief-spread parameters, the authors construct feasible truthful mechanisms and derive upper bounds for all exactly truthful, no-subsidy mechanisms, while also deriving first-price equilibrium revenues.

When a feasible lower bound for one design exceeds the upper bound for another, the ranking is certified. However, overlapping bounds do not establish which design generates higher revenue. Resolving these cases would require tighter analytical bounds, a sharper optimization of the truthful mechanism class, or a more precise characterization of the competing auction's revenue.