Second-price sealed-bid — dominant strategy truthfulness and revenue equivalence theorem
Auction Type
Vickrey (2nd price)
First price
Revenue equiv.
Bidders
Vickrey (second-price) auction: winner pays the second-highest bid. The dominant strategy is to bid truthfully — bidding your true value v is always weakly best regardless of others' bids. Proof: if you overbid and win when v < 2nd price, you lose money; if you underbid and lose when v > 2nd price, you forgo surplus.
Revenue equivalence theorem (Myerson 1981, Vickrey 1961): under standard assumptions (independent private values, symmetric risk-neutral bidders), all standard auction formats yield the same expected revenue to the seller. First-price and second-price auctions are equivalent in expectation.
The Vickrey auction is a cornerstone of mechanism design — it aligns incentives perfectly, making truthful reporting a dominant strategy (DSIC: dominant-strategy incentive compatible).