What this is

A one-day, paper-by-paper syllabus on how Amazon’s Sponsored Products auction works and how the machine learning around it is built - from the generalized second-price mechanism to autobidding theory, the prediction stack, reinforcement learning and generative bidding, Noam Brown’s search-plus-learning program, learning agents colluding or not, measurement inside an auction, and what Amazon has actually disclosed. Ten linked pages, about 150 papers, every claim cited to a fetched source. The parent essay is Amazon Ads, Deeply; the interactive companion is The Ad Auction, From the Inside.

Why a day, and why now §

Amazon’s advertising services line reached $68.6 billion in 2025 and grew 26% year over year in the second quarter of 2026 ^[1]. Almost all of it clears through auctions that run one search at a time. On August 31, 2026, the Federal Trade Commission and 22 states sued Amazon over how those auctions price clicks; Amazon’s response disclosed that about 92% of Sponsored Products placements in 2024 did not go to the highest bidder and that the mean winning bid ranked around 128th by amount ^[2]. Two parties are now describing the same mechanism in incompatible terms, in public, with numbers. There has never been a better moment to understand the machinery from first principles.

The literature that explains it is real, deep, and scattered across economics, operations research, machine learning, and game theory. A single essay cannot hold it. A day can.

Three threads to hold all day §

Every block below pulls on the same three threads. Keep them in hand.

1. The score is bid times quality, and each side owns one factor. Relevance-weighted GSP ranks by $b_i\cdot q_i$ and charges the minimum bid that would hold the slot. The platform owns $q$, a calibrated prediction. The advertiser owns $b$, ideally margin times predicted conversion. Every model in Block 3 is about $q$; every policy in Block 4 is about $b$; every theorem in Block 2 is about what happens when both are algorithms.
2. You never observe the counterfactual. The bid you did not submit has no logged outcome, the rival’s bid is hidden, the conversion arrives two weeks late, and the treatment leaks into the control. Block 7 is entirely about this; Block 5 argues it is the same problem poker solved.
3. Both sides are learning. The platform learns its mechanism; the bidders learn their policies; the advertisers learn what targets to give the bidders. Block 6 asks what such a market converges to, if anything.

The schedule §

Times assume a 7:30 start and generous breaks. Each block page opens with its own time budget and closes with a reading list, questions to carry forward, and full references.

If you have less than a day §

• Three hours. Block 1 in full, Block 4’s generative-bidding and benchmarks sections, Block 5’s bridges table, Block 8’s CPC decomposition, and the three-hour cut at the end of the bibliography.
• One hour. Amazon Ads, Deeply plus the time-budget callouts at the top of Blocks 2, 5, and 6.
• Fifteen minutes. The lab, then Block 8’s section on the two accounts of the auction.

How the day is built §

Each block is written as an essay, not a list: it states what a paper shows, why it matters for a bidder or a platform on Sponsored Products, and where the literature disagrees. Numbers carry a citation to a source that was fetched during the sweep that built this section; where a venue, an author list, or a figure could not be verified, the page says so in a parenthetical rather than smoothing it over. The sweep ran on September 2, 2026 using the Parallel research API for deep literature retrieval and independent verification agents that fetched each DOI, arXiv abstract, or Amazon Science page. Several identifiers circulating in earlier summaries turned out to be wrong and were corrected; several widely repeated numbers turned out to have no fetchable source and were dropped.

Two conventions. Claims about Amazon’s live auction come from three kinds of sources and are labeled as such: Amazon’s public documentation, Amazon’s response to the FTC, and the FTC’s complaint. None of them discloses the production formula, and the last two disagree. Transfers from other fields, above all from Noam Brown’s poker and Diplomacy work in Block 5, are marked as analogies with the assumption each depends on. Nothing in Block 5 is an established result about ad auctions.

Where to go afterward §

The open problems page turns the day into a week of building: a SODA-style equilibrium solver for position auctions with budgets, a piKL-leashed bidder with a per-keyword regularization schedule, an interference-aware experiment design for a bid-policy change, a landscape-model propensity estimator for deterministic auctions. Each has a first experiment that can be run this month with Amazon Ads API access, Marketing Stream, and an open simulator.

References §

1. Amazon. Q2 2026 earnings commentary on Amazon Ads growth. aboutamazon.com. Full-year figures from the 2025 Form 10-K. sec.gov
2. Amazon. Amazon’s response to the FTC’s lawsuit regarding Sponsored Ads. Aug 2026. aboutamazon.com. FTC press release, Aug 31, 2026. ftc.gov. Both are claims by parties to a lawsuit, not adjudicated facts.

Eternal Horizons · a reading day. Parent note: Amazon Ads, Deeply. Lab: The Ad Auction, From the Inside.