Efficiency

In the SPA and EA, bidders bid their true values and the bidder with the highest value wins the auction. So, the social surplus discussed earlier is equal to V1:n - the consumption value to the winner. This is the maximum social surplus that is possible in this situation. That makes SPA and EA efficient with the maximum expected social surplus of E[V1:n].

In the FPA and DA, too, the bidder who has the highest value bids the highest and wins the auction. So, these auctions are also efficient with expected social surplus E[V1:n].

Basically, in the IPV environment not only are the rules equivalent from an expected revenue maximizing auctioneer’s point of view, the rules are equivalent from social efficiency point of view, as well.