A Poet and His Auction
Long before William Vickrey won his Nobel Memorial Prize in Economics in 1996 for his work on auctions, a German poet Johann Wolfgang von Goethe was implementing auction strategies of his own. Goethe, a world-renowned German writer during the late 1700s and early 1800s, published a letter in 1797 that contained the details of a sealed-bid second-price auction. The letter was addressed to a popular publisher named Vieweg, and proposed Goethe’s plan to sell an epic poem called Hermann and Dorothea. In order to negotiate a fair price for his work Goethe proposed this in his letter: “…I will hand over to Mr. Counsel Bottiger a sealed note which contains my demand, and I wait for what Mr. Vieweg will suggest to offer for my work. If his offer is lower than my demand, then I take my note back, unopened, and the negotiation is broken. If, however, his offer is higher, then I will not ask for more than what is written in the note to be opened by Mr. Bottiger [Cited in Mandelkow (1968, p. 254)].
While Goethe’s auction contained only one potential buyer, Vieweg, Goethe’s own sealed demand acts as a second, sealed bid. Goethe’s strategy was that Vieweg would treat his sealed reserve bid as a random variable. Since this sealed value was unknown and independent to Vieweg, it was optimal for Vieweg to bid his true value. If Vieweg’s offer were higher than the sealed bid, Vieweg would simply pay the value of the sealed bid, or the second highest price. If Vieweg’s offer were lower than the sealed bid, the negotiations would be broken. “Goethe’s main aspiration was to reduce the informational asymmetry between author and publisher concerning the expected profit from a book: he wanted to learn about his “value” (Moldovanu, Tietzel p. 855). The auction strategy implemented by Goethe developed from this unbalanced relationship between authors and publishers: the publishers always knew the profit for themselves, but the authors were blind of their own values. By setting up this sealed-bid second-price auction, Goethe could let the offer made by Vieweg’s determine the valuation of his poem Hermann and Dorothea.
The auction itself had an interesting outcome. Mr. Counsel Bottiger, who had Goethe’s sealed bid, accurately predicted the value Goethe would put on his own work, and relayed this value to Vieweg. Vieweg then bid this value, so that the value of Vieweg’s bid and the value of the sealed bid were equal. The negotiations therefore held firm, and Goethe got exactly the value he asked for. While this result worked out well for both participants, Goethe could have benefitted more had he set up the auction in a different way.
In the case of Goethe’s auction, it would have been more beneficial for him to have as many bidders as possible participate in his auction. The bids would still need to be sealed and independently produced by each bidder, but Goethe would no longer have to submit his own sealed bid. “For the case of symmetric risk-neutral bidders with independent signals, Bulow and Klemperer (1996) show that an English auction with no reserve price (which is then revenue-equivalent to a second-price, sealed-bid auction) with N + 1 bidders is, in expectation, more profitable than any selling procedure with only N participants (Moldovanu, Tietzel p. 858). Simply having more bidders would increase the likelihood of Goethe receiving a high bid from one of the publishers, thus increasing the value of Goethe’s work.
http://www.jstor.org/stable/2990730?origin=JSTOR-pdf