For the painting:

(a) Yes, the average private value is equal to the expected painting value, because (20% + 10% + 0% −

15% − 15%)/5 = 0%.

(b) You should assume you are the one that had the 20% overestimate. Thus, if you know that there is exactly one bidder with the highest overestimate, it being exactly 20% of the value, then you should shave 20%

off your bid. In this example, if you have drawn $150, then you should offer no more than $150/1.2 =

$125.

(c) When you follow the instructions, you will find that with five bidders, your expected winning painting bid is about $111.7. So you should bid no more than $100/$111.7 ≈ 89.5% of your private value estimate. Here are more expected values of the top bid as a function of the number of bidders:

Number of Bidders 1 2 3 4 5 10 20 100 1,000 ∞

1,000-Row Average of $100 $105.7 $108.7 $110.2 $111.7 $115.4 $118.6 $124.8 $132.3 $138.4 Top Bid