The optimal strategy for a bidder in a private-values Vickrey auction is to bid his true valuation.

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In a private-values Vickrey auction, bidders have independent values for the item being auctioned and they do not know the values of other bidders. In this type of auction, the optimal strategy for a bidder is to bid his true valuation because the winner is the one with the highest bid but pays the second-highest bid amount. Therefore, if a bidder bids higher than his true valuation, he risks overpaying for the item. Similarly, if a bidder bids lower than his true valuation, he risks losing the auction and possibly not getting the item at a lower price. By bidding his true valuation, a bidder ensures that he pays a fair price for the item without overbidding or losing the auction.

The Optimal Strategy for a Bidder in a Private-Values Vickrey