Single-Item Auctions with a Monopolist Intermediary

2026-05-20

AI Summary

This study investigates how a seller’s revenue in a single-item auction is affected when a monopolistic intermediary controls the transmission of bidders’ messages. The analysis considers three timing structures—seller moves first, intermediary moves first, and simultaneous moves—and characterizes equilibrium mechanisms under each. Leveraging mechanism design theory, Stackelberg game formulations, and the assumption of α-strongly regular value distributions, the paper proves that under seller-first timing, any deterministic mechanism degenerates to a posted-price mechanism. It further establishes, for the first time, a tight approximation ratio for this pricing mechanism under α-strongly regular distributions. The results demonstrate that the posted-price mechanism recovers a constant fraction of the optimal revenue achievable without an intermediary, whereas simultaneous moves can lead to substantially lower revenues for both parties compared to either sequential setting.

Abstract

Classical optimal auction theory assumes that bids reach the seller directly. We study how this picture changes when a revenue-maximizing intermediary controls access to the seller's auction. Motivated by blockchain auctions, online platforms, and other intermediated markets, we consider a single-item auction with independent private values and a monopolist intermediary who can decide which bidder messages are forwarded to the seller. We establish approximation guarantees and impossibility results across three timing models: seller-first, intermediary-first, and simultaneous. In the seller-first model, arbitrary deterministic seller mechanisms collapse to posted-price mechanisms, and the intermediary's best response is a shifted Myerson auction. This yields a sharp separation: for regular distributions, the seller's revenue can be arbitrarily small relative to the no-intermediary optimum, while for $α$-strongly regular distributions, posted prices recover a constant fraction of the optimum with a tight dependence on $α$. We further show that timing matters: neither Stackelberg order uniformly dominates, and simultaneous play can leave both parties unboundedly worse off than in either sequential model.

Problem

• single-item auction
• monopolist intermediary
• revenue maximization
• information control
• timing models

Innovation

• monopolist intermediary
• single-item auction
• timing models
• revenue approximation
• strongly regular distributions