Affine fee-setting under worst-case buyer and seller distributions

Establish whether affine fee-setting mechanisms w(P) = (1 − α)P + β achieve a constant-factor approximation to the intermediary’s optimal revenue under worst-case choices of both the buyer value distribution and the seller cost distribution, thereby resolving the conjecture suggested by the prior literature.

Background

Prior work (LN07, LN13) identified conditions under which optimal fee schedules are affine and motivated their prevalence in practice. This paper proves constant-approximation guarantees for affine fee schedules under constraints on the buyer side (affine virtual value, MHR) for worst-case seller distributions.

A central unresolved question is whether affine fee schedules remain near-optimal in the strongest robustness sense—simultaneously against worst-case buyer and seller distributions. Confirming this would give a compelling theoretical justification for the ubiquity of affine fee-setting in two-sided markets.