Goethe and the Vickrey Auction

The specific—and likely unfamiliar—auction format used by the evildoers in Murder on the Serpentine Bridge, where the highest bidder wins but is required to pay only the price of the second highest bid, is known as a Vickrey Auction. The purpose of this structure, exactly as Kit Sheffield reasoned out in the pages of the book, is to cause each participant to make a sealed bid which reflects their own maximum estimate of the property’s true value, rather than trying to assess what the other participants may bid so as to avoid the possibility of offering more than is necessary.

This form of auction is named after William Vickrey, the economist who first described the dynamics of this type of process and other related matters of economic theory. He used so-called game theory to analyze how parties would logically respond to rules and incentives in such situations. Game theory is a mathematical method of modeling how rational decisionmakers make various strategic decisions. Vickrey won the 1996 Nobel Prize in Economics for his work.

Because game theory received in its initial full formulation in a 1944 book by John von Neumann and Oskar Morgenstern, while William Vickrey did his work even later in the twentieth century, it might seem that introducing a Vickrey Auction into a story set in the Regency Era is a clear anachronism. However, that is far from true!

As with virtually all breakthrough ideas, twentieth century game theory has antecedents in much earlier times. In 1838, Antonine Augustin Cournot published a mathematical solution for what came to be called “Nash equilibria”, a key advancement in game theory (more than a century later described generally by John Forbes Nash and made famous by the book and movie “A Beautiful Mind”). Even earlier, in 1713, Charles Waldegrave wrote an analysis of a then popular card game called “le Her” and outlined what is called in game theory “a minimax mixed strategy” (a description of which I will spare the Reader). The specific problem in this analysis is now known as a Waldgrave problem—in honor of Charles—though the problem was first described by Pierre Reymond de Montmort (1678-1719). So relevant aspects of game theory were not unknown at the time my story is set.

Even more relevant to the timing of the plot here is the recollection by both Charlotte and Wrexford of a similar approach to maximizing the price bid for a property previously used by Johann Wolfgang von Goethe. This is entirely based in fact. In addition to being perhaps the greatest figure in the history of German literature, Goethe was apparently no mean economist. In 1797 he had written a long epic poem he wished to sell to a publisher for the best possible price. The problem, as Goethe saw it, was that authors of his day had no idea of how many copies of their works were actually sold by publishers—information which the era’s publishers jealously guarded—and hence he had no idea of the potential profitability of their literary creation. (“The publisher,” Goethe complained, “always knows the profit to himself and his family whereas the author is totally in the dark.”) Our Nobel Laureate William Vickrey called this a problem of “asymmetric information”.)

Compounding Goethe’s problem was the complete absence of any meaningful copyright protection at this time. Even the most reputable publishing houses were then thought to put out multiple printings without informing or compensating their authors. Outright pirating of work by other publishers without any payment at all to the author was also rampant. The contemporaries of Charlotte and Wrex would very soon make meaningful improvements in this situation by the creation of a body of[copyright law at the Congress of Vienna.)

To get the highest possible price from his publisher Goethe came up with an ingenious strategy. He handed his lawyer a sealed note containing his own minimum demand for his poem. The publisher then bid for the work. If the publisher’s offer was lower than the number Goethe had put into the envelope (a number known only to Goethe and his lawyer) they would demand that the sealed bid be returned to Goethe without revealing the amount, and he would walk away from the deal. If the publisher bid more, however, he would secure the rights to the poem but only have to pay the lower amount Goethe had written in his sealed bid.

For exactly the reasons explained in our story, this left the publisher in the position of logically having to bid no less, though no more, than a fair share of the profits for Goethe, profits for which Goethe lacked the necessary information to calculate. Presumably, if Goethe had the envelope returned to him due to a too-low bid by the publisher he not only gained useful information but also had the opportunity to repeat the process with other publishers, thus effectively mirroring the auction mechanics of our story. Goethe has thus been credited in various analyses as having run the first known Vickrey Auction or near equivalent. It is thus entirely plausible that an ingenious criminal at the time of this story might have conceived of the auction process described in Pierson’s note.

Speaking of the brilliant but evil creator of our auction, Professor Milson-Wilgrom, I plead guilty in crafting his surname of having a little fun (if one can view the study of Economics, which Thomas Carlyle did after all deem “the dismal science”, as fun). The winners of the 2020 Nobel Prize for Economics were Paul Milgrom and Robert B. Wilson. They were cited in their award for  “improvements in auction theory and inventions of new auction formats.” I could not resist a little syllable switch to craft a hyphenated handle for our disreputable Professor. You may also remember that I named the Professor’s servant Vickrey, an homage to the economist who first analyzed this eponymous auction format.

Thus endeth, I promise, the discourse on Economic theory.