Consider a BeckerDeGrootMarschak (BDM) auction:

• You bid for a cap ranging from 0 to B
• A price is selected from 0 to B at random
• If your bid is greater than or equal to the randomly selected price, you get the cap and pay that randomly selected price
• If your bid is less than the price, you do not get the cap, and do not have to pay anything.

Proof that: your optimal bid that maximises the expected profit is V, where V0,B denotes your true subjective value of the cap.