The winner's curse in a bid war

MediumMarket Making & Betting Games~4m

You and one competing dealer independently price a hard-to-value block. Each of you forms an unbiased estimate of its true value $V$ : your estimates are independent and uniform on $[V-30,\,V+30]$ (so each is right on average). The block trades to whoever bids higher, so you only win it when your estimate is the larger of the two. Conditioned on winning, by how many dollars does your winning estimate overstate the true value $V$ on average?

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Winning conditions on your estimate being the larger - you need $E[\max]$ of the two noises, not either one.
For two i.i.d. uniforms on $[-a,a]$ , $E[\max] = a/3$ ; here $a=30$ .

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10 (± 0.001)

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The winner's curse in a bid war

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