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Auction Theory Lab

Equilibrium bidding and revenue equivalence

Compare equilibrium bid functions across first-price, second-price (Vickrey), and all-pay auctions. Simulate hundreds of auctions to verify revenue equivalence empirically.

Highest bidder wins, pays own bid. Equilibrium: shade bid below value.

Equilibrium bid: b(v)=n−1n⋅vb(v) = \frac{n-1}{n} \cdot v
Expected revenue (all formats, revenue equivalence): E[Rev]=n−1n+1=0.500E[\text{Rev}] = \frac{n-1}{n+1} = 0.500

Equilibrium Bid Functions

First-PriceSecond-PriceAll-Pay
0.000.250.500.751.00value (v)0.000.250.500.751.00bid b(v)

Revenue equivalence: under IPV with uniform distributions, all standard auction formats yield the same expected revenue E[Rev] = (n-1)/(n+1).

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Auction Theory Lab — Game Theory Labs · hbar.university