You value a painting at $600. In a Vickrey auction, you bid $800. The highest competing bid turns out to be $750. What is your payoff?
A+$600, because you won the item you wanted
B-$150, because you pay $750 for something worth $600 to you
C+$50, because your surplus is $800 minus $750
D$0, because overbidding in a Vickrey auction is always a dominant strategy
You win and pay the second-highest bid ($750), but the item is only worth $600 to you—a loss of $150. This is precisely the risk of overbidding: you occasionally win at a price above your true value, which is never worth it. A truthful bid of $600 would have lost this auction (to the $750 bidder), but that outcome is correct—winning at $750 when your value is $600 destroys $150 of surplus.
Question 2 Multiple Choice
Why does truthful bidding eliminate the strategic complexity that bidders face in first-price auctions?
AIn second-price auctions, all bidders observe each other's valuations before submitting bids
BYour optimal bid depends only on your own valuation, not on competitors' distributions or strategies
CThe auctioneer enforces truthful revelation through binding contracts before the auction starts
DSecond-price auctions have fewer participants, so strategic calculation is unnecessary
In a first-price auction, optimal bidding requires shading your bid below your value—and how much to shade depends on beliefs about competitors' valuations and strategies. In a second-price auction, truthful bidding is dominant regardless of what others do. Your payoff-maximizing bid is simply your own value. The payment rule renders competitors' information irrelevant to your bidding decision.
Question 3 True / False
In a Vickrey auction, a bidder who knows their valuation exactly has no incentive to deviate from bidding that valuation, regardless of what other bidders do.
TTrue
FFalse
Answer: True
This is what 'weakly dominant strategy' means: truth-telling is at least as good as any other bid for every possible configuration of competing bids. No information about competitors—whether you have it or not—can make a non-truthful bid better. This property is exceptional; most auction formats require you to form beliefs about competitors to bid optimally.
Question 4 True / False
Under standard assumptions, a seller earns higher expected revenue from a Vickrey auction than from a first-price sealed-bid auction, because bidders in first-price auctions shade their bids downward.
TTrue
FFalse
Answer: False
The revenue equivalence theorem shows that both auction formats yield identical expected revenue under standard assumptions (risk-neutral bidders, independent private values, symmetric equilibrium). In first-price auctions, bidders shade their bids but pay what they bid; in Vickrey auctions, bidders bid truthfully but pay the second-highest bid. These effects exactly cancel in expectation.
Question 5 Short Answer
Why is bidding below your true valuation also a mistake in a Vickrey auction, even though it seems to protect you from overpaying?
Think about your answer, then reveal below.
Model answer: Bidding below your value risks losing auctions you should win. If a competing bid falls between your true value and your understated bid, you lose even though winning would have been profitable—since you would have paid the competitor's lower bid. The Vickrey payment rule already protects you from overpaying: you always pay someone else's bid, not your own, so there is nothing to gain by understating your value and much to lose by missing profitable wins.
The dominant strategy proof covers both directions: bidding above value introduces the risk of winning at a loss, while bidding below value introduces the risk of missing a profitable win. Only truthful bidding avoids both failure modes simultaneously, for every possible realization of competing bids.