Simulate English, Dutch, sealed-bid, and Vickrey auctions with multiple bidders. Explore revenue equivalence and winner curse.
This simulator takes a set of bidder valuations and runs them through four auction formats side by side: English ascending, Dutch descending, first-price sealed-bid, and second-price sealed-bid (Vickrey). Sealed-bid formats don't take arbitrary typed bids; they apply the symmetric Nash equilibrium bidding strategy for the value distribution selected, shading bids below value for first-price and bidding truthfully for Vickrey. The thing most people get wrong: they expect every format to charge the same price on a single run. Revenue equivalence is a statement about expected revenue averaged over many auctions, not about any one outcome, so first-price and second-price results will legitimately differ trial to trial.
A concrete input and expected output from the current implementation.
Input
4 bidders, independent private values drawn from uniform[0,100]: 80, 65, 50, 30. Run first-price sealed-bid, second-price sealed-bid (Vickrey), English, and Dutch on this same value set.
Expected output
Winner is the bidder valued at 80 in all four formats. First-price and Dutch clear at 60 (equilibrium bid = value x (n-1)/n = 80 x 3/4). Second-price and English clear at 65 (the second-highest value).
With n=4 uniform values, the symmetric first-price/Dutch equilibrium bid function is b(v)=v(n-1)/n, so the top bidder bids 80*0.75=60; Vickrey and English are strategically truthful, so the winner pays the second-highest value, 65.
You supply each bidder's private value directly, or draw N values from a chosen distribution (commonly uniform). For first-price and Dutch formats the tool converts each value into its symmetric Nash equilibrium bid rather than bidding the raw value, since bid shading is what rational bidders do in those formats. For second-price and English, it bids the value itself because truthful bidding is a dominant strategy there.
Given the bids, each format's clearing rule determines the winner and price: highest bid wins and pays its own bid (first-price, Dutch), or the highest bid wins but pays the second-highest bid/value (second-price, English). Running the simulation across many repeated value draws accumulates an average revenue per format, which is what actually converges under the revenue equivalence theorem, not any single auction.
That's expected on a single run. Vickrey's rule charges the winner the second-highest value, while first-price bidders rationally shade below their own value to leave a margin. The two formats only match in expected revenue averaged over many auctions, not bid for bid.
Not directly. It's an educational simulator built on textbook assumptions - risk-neutral, symmetric bidders with independent private values - that real sales often violate through collusion, budget constraints, or correlated valuations, so treat its comparisons as illustrative rather than a procurement recommendation.
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