Values That Lean High
Two risk-neutral bidders have independent private values with cumulative distribution F(v) = v² on [0, 1]. They compete in a sealed-bid first-price auction (the high bid wins and pays its bid) and play the symmetric equilibrium. What is the seller's expected revenue? Give a reduced fraction.
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Source: Original problem written for AxiomIQ; uses the standard first-price equilibrium formula and the revenue equivalence theorem.