Auction Theory: Four Canonical Formats and Revenue Equivalence

Overview

Auction theory analyzes strategic bidding behavior across different selling mechanisms. The four canonical formats — English (ascending), Dutch (descending), first-price sealed-bid, and second-price sealed-bid (Vickrey) — generate identical expected revenue under standard assumptions. The Revenue Equivalence Theorem (RET) is the central benchmark; deviations from its assumptions drive all practical auction design decisions.

When to Use

• Choosing among auction formats for selling goods, spectrum, procurement, or ad slots
• Analyzing bidder strategy (bid shading, sniping, jump bidding) under a specific format
• Evaluating whether a proposed auction achieves optimal revenue or efficiency

When NOT to Use

• Posted-price or negotiated sales where no competitive bidding occurs
• Multi-unit auctions with complex complementarities (use combinatorial auction frameworks)
• The seller has no commitment power to enforce auction rules

Assumptions