Long before the birth of game theory, a German author designed an auction for his book. What happened next will astound you.
Johann Wolfgang von Goethe (1749-1832) was arguably the greatest German writer, poet and polymath of the Romantic era. His forays in science, diplomacy, literature etc are well-known. His dabblings in the applied economics and auction design are less known however.
One incident in particular is worth mentioning. While selling the publishing rights of his epic poem ‘Hermann and Dorothea’, Goethe had made an intriguing proposal to his publisher. According to this proposal, Goethe would submit his reserve price in a sealed envelope. The publisher was asked to quote how much he was willing to pay for the publishing rights of this poem. If the price quoted by the publisher turned out be greater than the reserve price asked by Goethe, the deal would be finalised. The publisher would get the publishing rights of ‘Hermann and Dorothea’; Goethe would receive the amount he asked (not the amount the publisher quoted) as royalty. If the publisher’s quote turned out to be lower than Goethe’s reserve price, the negotiation would be broken and there would be no deal.
For many decades, this proposal remained a mystery. Why conceal your reserve price in a sealed envelope? Why not state it upfront and make a ‘take it or leave it’ offer to the publisher? And once the publisher has indicated a much higher figure, why settle for the lower reserve price as royalty? Few were able to solve this puzzle. The consensus was that the entire scheme was whimsical and devoid of any logic.
The puzzle was resolved by the game-theoretic analysis of auctions in the recent years. Game theory is a discipline that studies the interpersonal decisions-making formally. Although extremely broad in scope, the actual predictive power of game theory is limited by two factors.
First, it assumes a structured situation. By a structured situation, I mean that individuals’ goals, their actions and outcomes of those actions are precisely defined and assumed to be known. Second, individuals are assumed to be rational: they are expected to pursue their goals like an automaton with a single-minded devotion and ruthless efficiency.
In reality, both these assumptions are rarely satisfied. Most of the social interactions are somewhat fuzzy and amorphous; there is neither any definite objective, nor a given plan of action. Second, the stakes in typical interactions are so small that it is rarely worthwhile to do the kind of cost-benefit analysis and strategizing that game theory takes for granted.
Auctions are a domain that satisfy the assumptions of game theory. Auctions are typically structured situations where elaborate rules determine what kind of actions are allowed, what will be the outcome if certain actions are followed etc. Usually, the amounts at stake are huge; it is worthwhile to spend resources in strategizing. Consultants are hired; various contingencies are thought through and gamed; dummy auctions are run etc. The bottom line is that many cognitive biases that affect individual decision-making are eliminated, and the participant’s behaviour is rational in a textbook sense. No wonder, auctions have turned out to be a promising area where game theory is immensely successful.
The key to understanding Goethe’s proposal lies in the game-theoretic analysis of the first-price and second-price auction formats. In a first-price auction, the highest bidder wins the object and his bid becomes the price. In a second price auction, the highest bidder wins the object, but the highest losing bid becomes the price. Why would anybody choose such a bizarre format? It turns out there are good reasons.
To understand, suppose there is an object, say a rare painting. You estimate the painting is worth say Rs 10 million. How much should you bid in a first price auction? Clearly, it should be strictly less than 10 million. Why? Think about it, in an auction either you win or you lose. If you lose, then you neither get the painting nor pay anything. Your net benefit is zero, irrespective of your bid. But if you win, you get the painting and pay your bid. Your net benefit is positive if (and only if!) your bid is strictly less than your value. How much less than your estimate should an optimal bid be? It depends on a number of factors like how many bidders there are, how strong/aggressive they are etc.
By contrast, in a second=price auction, life is much simpler due to a striking result. In such an auction format, the best you can do is to bid your estimate (Rs 10 million) truthfully, irrespective of what competing bids are.
The logic is as follows: the highest competing bid will be either less than or greater than your estimate. Should you win the auction, this bid will become the price. If the highest competing bid is less than your estimated value, you don’t want to bid lower than the competing bid. Otherwise, you will miss buying the painting at a lucrative price.
Similarly, if the highest competing bid is greater than your estimate, you won’t want to bid more than the competing bid. Otherwise, you’ll end up paying more than what you think the painting is worth. The best way of achieving these objectives is to bid exactly what your estimate of the painting is; not a penny more or less.
In short, in a second-price auction, truth-telling is a dominant strategy. It doesn’t matter how many competing bidders you have; it doesn’t matter how intelligent or stupid your rivals are; it doesn’t matter how rich or poor they are; it doesn’t matter how aggressive or docile bidders they are. All that matters is what you think an article is worth and you go ahead and bid it.
Back to Goethe. Apparently, von Goethe knew this ingenious property of the second price auction. In those years, there was an inherent informational asymmetry between the author and the publisher. While the publisher knew exactly how many copies of the book written by an author sold and how much profit they earned, the author had no idea about these things. Consequently, the negotiation between the author and the publisher was rigged in the favor of the publisher.
Goethe was determined to remedy this situation. He was not only interested in getting higher valuation for Hermann and Dorothea; he was also interested in learning how much his writings were worth commercially. Simply asking this information won’t work: his publisher would have obviously understated his profit. By concealing the reserve price, Goethe had contrived a situation where the publisher’s problem was exactly like a participant in the second price auction with one competing bid. By the reasoning outlined in previous paragraphs, it was best for his publisher to bid truthfully, revealing Hermann and Dorothea’s commercial value.
It was a brilliant design, and yet it failed to achieve the intended outcome. The reason was a factor that even someone as intelligent as Goethe had overlooked: the integrity of the auctioneer. Apparently, the person Goethe had engaged to run this auction was a double agent. He had indicated to the publisher what Goethe’s secret reserve price was likely to be. Given this information, the publisher’s problem was simple: just bid the reserve price, frustrating Goethe’s scheme to find out his worth.
Before you rush to judge his dabblings in auction design, let me add that it was a noble failure. Like Da Vinci’s sketches of the helicopter in the fifteenth century and Heron’s inventions of the steam engine some two thousand years ago, Goethe failed because he was thinking far ahead of his time. Even his failure illustrated two key lessons of the practical auction design. Importance of the integrity of auctioning process is one of them; the other is the benefit of attracting many bidders. Goethe’s auction would not have failed, had he invited a few more bidders. Even today, this insight is often forgotten: Think about the ‘blacklisting rules’ in weapon-procurement auctions.
Towards the end of his career, Goethe did understand those lessons. He organized another auction for the publication rights of his collected works. This time, he was an established author at the height of his popularity. Consequently, the auction attracted more than thirty publishers. This auction was a runaway success, and it made von Goethe a rich man.