One not-so-intuitive result in auction theory is the revenue
equivalence theorem, which states that as long as an auction
complies with some conditions, it will on average generate the
same revenue to an auctioneer as the revenue generated by any
other auction that complies with them. Surprisingly, the conditions
are not defined on the payment rules to the bidders but on the
fact that the bidders do not bid below a reserve value—set by
the auctioneer—the winner is the one with the highest bidding and
there is a common equilibrium bidding function used by all bidders. In
this paper, we verify such result using extensive simulation of a
broad range of auctions and focus on the variability or
fluctuations of the results around the average. Such fluctuations
are observed and measured in two dimensions for each type of
auction: as the number of auctions grows and as the number of
bidders increases.
Equivalence theorem of D-optimal equal allocation design for multiresponse mixture experiments
