Consider a Becker-DeGroot-Marschak (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 , where denotes your true subjective value of the cap.