Like the inverse of one-upmanship. For example, if you mention that you're a little short on money this month and then a certain type of friend begins to discuss how they are the single poorest person to ever walk the earth as if to prove they are much more efficient at being living in poverty.
It might just be "one-upmanship" but I'm curious to know if there's a word for when a said person seemingly wants to appear worse off or in a worse position than someone else.