Auctions and Mechanism Basics
An auction is a game whose rules someone chose. Change the rules and optimal behaviour changes with them, which is the subject of mechanism design and is worth one lesson here because two formats come up constantly.
First-price sealed bid
Everyone submits a bid, the highest wins and pays what they bid.
Bidding your true value guarantees zero profit: you either lose, or you win and pay exactly what it was worth. So everyone shades below their value, and the shading depends on how many rivals there are and what you think they will do. In a private-value setting, where the item is worth a different amount to each bidder, more competition means shading less, since you need to bid nearer your value to win at all.
Note this is the opposite direction to the winner's curse, which lives in common-value settings where the item is worth the same to everyone and more competition means shading more. Two forces, two settings, opposite signs. Keeping them apart is worth doing deliberately.
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