Goethe was a Game Theorist

A favorite professor of mine once told me that it's always impressive to start with an example from the 18th century. So in deference to him and with a nod to Jonah Lehrer's forthcoming book, I'd like to mention Goethe's anticipation of one of the pillars of auction theory, as elaborated in an article by Moldovanu and Tietzel in JPE 1998.

In 1797, one of the central features of the book market in the (not yet unified) German states was the absence of copyright protection. An author sold his work to a publisher for a set fee, thereby fully relinquishing his rights to it. Publishers could print and sell as many copies as they wished, without ever giving more money to the author than his original "sheet royalty". It was therefore very difficult for an author to know exactly how much he was worth in the growing market for literature. Goethe, clever man that he was, set up a brilliant experiment to get around this asymmetry of information.

"I am inclined to offer Mr. Vieweg from Berlin an epic poem, Hermann and Dorothea, which will have approximately 2000 hexameters....Concerning the royalty we will proceed as follows: 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."

Those of you who are familiar with auction theory will recognize this as a second-price auction, with Goethe himself effectively playing the part of the second bidder! In such an auction, the person making the highest bid wins the item on the table, but pays only the second-highest bid. When there is uncertainty about the other bidders' valuation of an object (as there is here where Mr. Vieweg does not know the sum Goethe has sealed in the envelope), each player can do no better than to bid exactly what the item is worth to him. If he bids lower, he risks losing the item when he would have been willing to pay more for it. If he bids higher, he risks the second-highest offer's being between his offer and his true valuation, in which case he pays more for it than he thinks it is really worth. With this brilliant set-up, Goethe did guarantee that he could earn no more than what he had committed himself to in the letter, but what he hoped to gain was information about his true worth to the publisher. And for a man who planned to write future books, such information would have come in handy in future negotiations.

It should here be noted that sealed-bid, second price auctions were only formally analyzed in 1961, and that that analysis in large part earned William Vickrey the Nobel Prize in Economics.

For those who are curious as to whether Goethe's foresight and ingenuity payed off...well, unfortunately he chose his third-party badly. Counsel Bottiger opened the envelope and sent a friendly letter to Mr. Vieweg suggesting that he could bid as he wished, but surely no less than 200 Friedrichs d'or, which was by amazing coincidence the exact sum in Goethe's envelope. Et tu, Bottiger?