vector to the monotone price benchmark, the maximum revenue that can be obtained from a bid vector using supply-respecting prices that are nonincreasing in the bidder ordering and bounded above by the second-
highest bid. As a consequence, our auctions are simultaneously near-optimal in a wide range of Bayesian multi-unit environments.
Joint work with E. Koutsoupias, J. Kulkarni, S. Leonardi, T. Roughgarden and X. Xu.