Goethe’s Price Games, Auctions, and Other Surprises

Abstract

This chapter is dedicated to Goethe’s price game which can be interpreted as a second-price sealed-bidauction. Nobel Laureate William Vickrey has shown for this type of auction that bidding one’s willingness-to-pay price is an optimal strategy. We do not know whether Goethe had a similar result in mind. In fact, his sealed-bid price functioned like a take-it-or-leave-it option. Given the historical circumstances, it implied price-fixing, thereby avoiding explicit bargaining. A discussion of the Revenue Equivalence Theorem adds some theory to Goethe’s auction setting. The theorem says that, in principle, first-price sealed-bidauctions, Dutchauctions, second-price sealed-bidauctions, and Englishauctions pick the same winners and have identical prices. There are other types of auctions as well, and some have rather peculiar effects. All-payauctions are recommended for exploiting bidders—as in collecting money for a charity. If you want to win, do not participate. English auctions can have peculiar results, too. You might be interested in paying a high auction price for Gauguin’s “Mata Mua” if you already have a number of Gauguin paintings in your collection. On May 9, 1989, the “Mata Mua” was auctioned by Sotheby at 24.2 million dollars, then being the highest price ever bid for a Gauguin painting. You might also be willing and able to pay a high auction price if you represent a consortium of the Federal Republic of Germany, the States of Lower Saxony and Bavaria, the Prussian Cultural Heritage Foundation, and private donators. On December 6, 1983, the gospel book of Henry the Lion (1129–1195) was auctioned and sold for a price of £8,140,000, then equaling 32.5 million German marks. There was a single bidder present in the auction hall, i.e., the representative of the consortium, and a second person calling bids from outside—possibly the seller.