Consider a first price sealed auction where the bidders' valuations are drawn from a uniform distribution $[0, \bar{v}]$. As the number of bidders increases, so does the expected value of the highest bid.

Question

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In a first-price sealed auction, as the number of bidders increases, the competition among bidders also increases. Given that their valuations are drawn from a uniform distribution, the probability of having higher bids also increases because there are more samples being drawn from the distribution. Therefore, the expected value of the highest bid increases with the number of bidders.

Consider a First Price Sealed Auction Where the Bidders' Valuations [0,vˉ][0, \bar{v}][0,vˉ]

Consider a First Price Sealed Auction Where the Bidders' Valuations $[0, \bar{v}]$