In a sealed-bid auction with private values drawn independently from a common distribution, each buyer's equilibrium bid is set equal to:

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In a sealed-bid auction with private values, the equilibrium strategy for each bidder is to bid slightly below their own valuation of the item, specifically, at the expectation of the next-highest bidder's value conditional on it being smaller than their own. This strategy ensures that a bidder maximizes their payoff by winning the auction only when it is beneficial for them, considering the competition's likely valuations.

In a Sealed-Bid Auction with Private Values Drawn Independently from a Common