  I consider a mechanism design problem of selling multiple goods to multiple
bidders when the designer has minimal amount of information. I assume that the
designer only knows the upper bounds of bidders' values for each good and has
no additional distributional information. The designer takes a minimax regret
approach. The expected regret from a mechanism given a joint distribution over
value profiles and an equilibrium is defined as the difference between the full
surplus and the expected revenue. The designer seeks a mechanism, referred to
as a minimax regret mechanism, that minimizes her worst-case expected regret
across all possible joint distributions over value profiles and all equilibria.
I find that a separate second-price auction with random reserves is a minimax
regret mechanism for general upper bounds. Under this mechanism, the designer
holds a separate auction for each good; the formats of these auctions are
second-price auctions with random reserves.
