The optimal bid for an individual participating in a first-price,sealed-bid auction with independent private values is to bid:

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In a first-price, sealed-bid auction with independent private values, each bidder only knows their own personal valuation of the item. Therefore, the optimal bid is to bid less than their valuation in order to potentially win the item at a lower cost. If the bid is exactly or more than their valuation, they may win the item but at a cost higher than their own perceived value. It is important to note that the exact optimal bid may vary depending on the individual's specific valuation and beliefs about the valuations of other bidders.

The Optimal Bid for an Individual Participating in a First-Price,sealed-Bid