Here is an example of IPV auction that I often use in my classes. I give each student a coupon that has a dollar number written on it. The dollar numbers are randomly generated from {1, 2, …, 10}, all with independently and with equal probabilities. I ask the students to not show their coupons to others so that their numbers are private information to them.
I ask the students bid for the object on sale – a certificate that I place on my table. This is real bidding, and the students bid for the certificate with their own money under a stated auction rule. The student who wins the certificate has to paste her coupon on the certificate and return it to me. In exchange I give the student the dollar number that is now shown on the certificate. The students who did not win the auction just throw their coupons (hopefully into the recycle bin).
If there are n students and V1, V2, …, Vn are the numbers on their coupons then they have an IPV situation with values V1, V2, …, Vn for the object on sale. The values are independently distributed according to some distribution F(.) (in my case uniform over integers 1 to 10). Bidder i knows her value Vi privately, and believes that the values of the other bidders are random variables with distribution F(.). This precisely describes the IPV environment.
Risk Neutral bidders and seller
In what discuss we also assume that the bidders and sellers are risk neutral. So, if they expect to receive $10 and $0 with equal probabilities then the maximum amount that they would be willing to pay for the gamble is $5, the expected return from the gamble.