I know that 2nd-price auction is truth-telling, but 3rd-price auction is not.
What If I run the regular 2nd-price auction, in the end, the winner is charged at the 2nd bidding price with a discount, say 10% off. Is truth-telling is a dominant strategy for this type of auction?
For example, with bids being 10, 5, 4, and a fixed discount 10%, the winner will be charged 5*0.9 = 4.5
(This is an extension to this question: Third and average price auction)
An equilibrium will be one where everyone bids 11.11% more than their valuation. That is, a bidder with private valuation $p$ reports $p/0.9$. Everyone is bidding more than private valuation, but the information revealed is same as in a regular 2nd-price auction.