How to Auction a $1 Bill?

In my previous blog on sunk costs, I used the example of auctioning a $1 bill. I received some e-mails on this topic requesting clarification. Here is a quick clarification and analysis.

The goal is to auction a $1 bill to the highest bidder. Bidding can start in increments of 10 cents with an initial price of 10 cents. A $1 bill at 10 cents is quite a lucrative deal. However, this is an auction with a slight twist, which is announced at the start of the game. The twist is that the second highest bidder too will have to pay the amount of his or her second highest bid to the auctioneer, when the bidding ends. Of course, the second highest bidder does not win the $1 bill but he or she still has to pay up.

Generally, several people join the bid and the bid pretty quickly moves up to 90 cents. This is when most the people drop out of the auction and only the highest and the second highest bidders are left in the game. At this point the second highest bidder, lets call her Ashley, realizes that she will end up losing her 80 cents unless she bids at $1, which she thinks is still a better alternative than losing 80 cents. This is an easy decision for Ashley and she raises her bid to $1. Now the other party, lets call him Hank, follows the same logic as Ashley and realizes that for him it is still better to raise his bid to $1.10 instead of losing 90 cents. Again an easy decision for Hank. Now Ashley is about to lose her $1 but if she wins the next bid at $1.20, her loss will be only 20 cents. Ashley raises her bid to $1.20. Please note that competitiveness is playing no part here. These two individuals are trying to be as rational as possible to minimize their total loss. When the bid reaches $2 for a $1 bill, Hank, who is now the second highest bidder reasons that if he bids $2.10, his loss will be only $1.10 otherwise he will be losing $1.90. This can continue for a long time until one of them realizes ridiculousness of the situation.

What is the problem here? The problem is that Ashley and Hank are calculating their loss based on sunk costs. However, loss or gain should be calculated on future costs or gains only. Once we exclude sunk costs or costs incurred in the past, the quality of decision improves substantially. When the bid amount reaches $1, no one will be willing to bid on it, since sunk costs are no longer a factor in decision making. Therefore, Ashley or Hank will just pay up 90 cents to exit the game. In fact, the people who think through and realize that this game is based on escalation of commitment won't play the game. Another solution to this game is that if the first person bids $1 on a $1 bill, there won't be any second highest bidder and the game will end.

In business such situations are quite common. For example, a project that never seems to end. Past investments or past efforts in such cases should be given no consideration, when a decision about future has to be made. Analysis should be based on incremental costs and gains.

What are Sunk Costs?

There was a rich knight in the court of an agreeable king. One day the king got mad at the knight. Since the king had known the knight for a long time, he described three punishments to the knight and allowed him to choose one. The three punishments were caning, eating a gallon of farm fresh manure or expulsion from the kingdom. The knight accepted caning but half-way through caning realized that he would possibly not survive the full course of caning. Therefore, he begged the king to allow him to choose another punishment. The kind king agreed and the knight asked for a gallon of manure. After consuming half a gallon of manure, the knight felt dizzy with nausea and knew that he would certainly die, if he were to eat the whole gallon. Therefore, he begged the king to expel him from the kingdom. Our kind and immensely agreeable His Majesty agreed again. He then expelled the knight from the kingdom, asked IRS to attach his property to the government treasury and lived happily ever after.

Many people tell me that the knight was an idiot. If he had known his limitations, he could have chosen to leave the kingdom in the first place without suffering the ignominy of caning or eating the humble cow pie. I disagree since this conclusion is based on hindsight, while life choices have to made with foresight. I think that the knight was a bright smart cookie, who was willing to take risks and explore his limitations. Best of all, he was not afraid to take a loss and get out at the right time. By doing this he avoided the worst case scenario, which could have been the loss of his rear-end or death. Half way through caning, he accepted caning as his sunk cost, realized that enough was enough, took the loss and got out of the market. His next venture was equally disastrous but he knew when enough was enough and got out in time.

Most of us have trouble realizing when enough is enough and continue to throw good money after bad until we are overwhelmed by the worst case scenario. We keep on pouring money into projects several months after the return on investment has turned negative. Often the only rationale is that we have already invested several millions in this project, why not a few hundred thousand more to finish it. When you come across this logic, try to extend it ad infinitum and you will quickly realize the futility of such logic.

At several parties I have auctioned a one dollar bill for six to eight dollars before people realized that they were really being stupid. I begin auctioning a one dollar bill at the starting bid of 10 cents with a condition that I'd also seize the bid amount from the second-highest bidder. For instance, when the highest bid reaches 70 cents, the second-highest bidder realizes that he would lose his 60 cents, unless he raised his bid. Eventually, the bid for a one dollar bill reaches $1 and the second-highest bidder at 90 cents reasons that his loss would be 90 cents if he did not bid. On the other hand, if he won the bid at $1.10, he would only lose 10 cents. This reasoning continues with disastrous results for the bidders and usually they end up paying several dollars to me for a one dollar bill. Human behavior is not designed to accept sunk cost. Humans are inveterate loss-avoiders and have deep trouble accepting the notion of sunk cost.

I have another way of looking at the sunk costs using the notion of time machine. I say that I wouldn't worry about the past until I got a time machine that would allow me to go back in the past and fix things. Until that time, we can only change the future. Therefore, let's work on changing the future.