The easiest way to understand IPV environment is to consider the auction game that I play in my lectures.
In this game I give out coupons to my students each indicating a dollar number. The numbers are randomly generated between $1 and $10. The students bid for a certificate that I place on my table in the classroom. A student who wins the certificate sticks her coupon at the bottom of the certificate, returns it to me and receives the dollar amount stated her coupon. The remaining coupons from other students go to the trash can.
What is the object on sale?
:The certificate.
What is a bidder's value from winning the certificate?
: The amount indicated on her coupon.
Each bidder's value for the certificate is private - other bidders don't know the amount written on her coupon.
Ther bidders' values are independent and distributed randomly between 1 and 10.
Literally, that is how the numbers have been generated. I tend to use the uniform distribution for the random number generation process.
Yes, this is the extent to which I have to go to create an environment where the bidders' values are private and independently distributed according to the uniform distribution. I cannot give example from real life that is this pure.