Auction Theory

Compare auction formats, discover revenue equivalence, and see the winner's curse

Auctions as Games

Four ways to sell an item, four different ways to bid. Yet on average the seller takes home the same amount.

Revenue Equivalence

Set the number of bidders and trials, then press Run Auctions. Watch the revenue distributions of all four formats converge on the same average.

Go deeper:Auctions as Games

An auction is a game where bidders compete to buy an item. Each bidder has a private valuation — the most they're willing to pay — and must decide how much to bid. Different auction formats produce different strategic incentives.

The four standard formats are: English (ascending price), Dutch (descending price), first-price sealed-bid(highest bid wins, pays their bid), and Vickrey (highest bid wins, pays the second-highest bid).

One of the most surprising results in auction theory: under standard assumptions (risk-neutral bidders, independent private values), all four formats generate the same expected revenue for the seller.

Go deeper:Strategic Differences
  • Vickrey (second-price): Truth-telling is a dominant strategy. You should always bid your true valuation, because you only pay the second-highest bid if you win.
  • First-price: Bidders shade their bids below their valuations. When valuations are drawn independently and uniformly, as in this simulator, the optimal bid in a Bayesian Nash equilibrium is (n-1)/n of your valuation with n bidders.
  • English: Strategically equivalent to Vickrey — the winner pays just above the second-highest valuation.
  • Dutch: Strategically equivalent to first-price — you must decide when to stop the clock, just like choosing a sealed bid.

Key Takeaways

  • Revenue equivalence — all standard auctions yield the same expected revenue
  • Vickrey insight — second-price auctions make honesty the best policy
  • Bid shading — in first-price auctions, rational bidders bid below their valuation

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