First-price, Vickrey, and common-value auctions, bidding strategy and the winner's curse.
Warming up the engine…
The design and strategy of selling under competition: first-price (bid your shaded value), second-price/Vickrey (bid your true value), and common-value auctions (beware the winner's curse).
Vickrey: truthful bidding is dominant; Revenue Equivalence: standard formats yield equal expected revenue
In a second-price auction your bid only sets WHETHER you win, not what you pay, so honesty is free. In common-value settings, winning is bad news, you were the most optimistic estimator, so rational bidders shade down.
Say WHY truth-telling is dominant in Vickrey (your bid never affects your price), not just that it is.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at v 60, b 45.
Equilibrium: v* = 60.0, b* = 45.0
Current equations
You value the item at the orange line. Bid that much and winning earns you nothing, so in a first-price auction you shade your bid below your value. The blue line shows the optimal shading: with three rivals, bid about three-quarters of what it is worth to you.