Single-Item Auctions with a Monopolist Intermediary
For auction designers and platform operators, this work provides the first approximation guarantees for intermediated auctions, revealing how intermediaries can drastically reduce seller revenue and how timing of moves affects outcomes.
This paper studies single-item auctions with a revenue-maximizing intermediary who controls bidder access to the seller. It shows that in the seller-first model, the seller's revenue can be arbitrarily small relative to the no-intermediary optimum for regular distributions, but for α-strongly regular distributions, posted prices recover a constant fraction of the optimum with tight dependence on α.
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.