I argue that the auctioneer must make a net payment, in general, to the bidders in a second price double auction. That argument is in the context of a diverse goods auction and is thus very complex. Here I will try to substantiate that strange result in a simpler context.

The second price auction normally presumes several buyers and some unknown benevolent seller, whose motives seem to be distribution of fixed goods to those who value them most. We seek here a dual of that auction for sellers; auction rules that remove their incentive to state a higher price than they would actually be willing to accept, in hopes of getting more. Dually we postulate a benevolent buyer who must buy some fixed amount and wishes to compensate those needing most to sell.

To be the dual of the buyer’s auction, the seller must be motivated to submit a sealed bid mentioning the minimal price that he would sell it for without fear that mentioning a lower price will result in less income. If there are several sellers, each submitting sealed bids, and one buyer, then the bidder submitting the lowest price delivers his goods and receives in payment the price submitted by the second lowest selling bidder. Such rules seem to provide the seller incentives.

Now imagine that there are two each with a 1929 Cord automobile to sell. One is willing to give it up for $40,000 but the other requires $60,000. There is one buyer who is willing to pay $80,000. Our rules say that the first seller gets $60,000 for his car. The seller is happy but the buyer may not be.

We can now see why the auctioneer must provide a net payment for a second price true double auction. If neither party is to fear telling the truth, the auctioneer must pay the seller what the bidder truly thinks the goods are worth, while collecting from the buyer only what the seller was willing to settle for.

For a second price double auction where both buyers and sellers have incentives to bid their true value, it seems that the auctioneer must make up the difference. Such is hardly a viable occupation. I have considered schemes where buyers and sellers somehow pay the auctioneer on the side but this does not seem to solve the problem equitably.