The authors study auctions in unlimited supply. They show that no constant-competitive truthful auction is envy-free. They also show that by relaxing the problem to instead being truthful with small probability of being envy-free, or vice versa, auctions can be competitive.
Definitions:
Truthful: any bidder's best strategy is to bid the maximum value they are
willing to pay
Envy-Free: after the auction is run, no bidder would be happier with the
outcome of another bidder