Single-Item Auctions with a Monopolist Intermediary

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 $\alpha$-strongly regular distributions, posted prices recover a constant fraction of the optimum with a tight dependence on $\alpha$. 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.