The dollar auction, or out of the frying pan into the fire

When a decision maker lacks in intellect, judgement or character, these weaknesses are likely (though not certain) to be reflected once his or her decision is put into effect, so it comes as no surprise that organizations with poor leadership are often unsuccessful in their endeavors. Sometimes, however, bad results are achieved even when the decisions that led to them were made by smart leaders in a rational manner and were based on an in-depth analysis of factual data. Either way, once the milk is spilled and it becomes clear that things have gone wrong, the right course of action is to acknowledge the reality, stop the venture, and carry on.

In best practice organizations, such bad experiences are not only stopped early, but they are also treated as learning opportunities. If root causes of the failure are not immediately obvious, an impartial, fact-based analysis is conducted, often leading to useful conclusions (lessons learnt) which are widely shared so that they can be leveraged in future undertakings. If anyone gets punished at all, it is because of their obvious negligence, gross violation of important rules, or other unprofessional conduct, and not because they didn’t succeed despite their best efforts.

In those organizations which cannot quite boast of being best practice ones, the truth is often swept under the carpet, probably because facing the actual causes of a failure could be embarrassing for too many important people. When the situation eventually becomes too bad to continue pretending otherwise, the failure may well be blamed on a scapegoat, as discussed in the previous post. It is instructing to take a look at what often happens in-between, i.e., when negative results of a decision are already becoming visible, but the failure of the initiative is not yet acknowledged.

Specifically, we are not considering a situation when certain costs have been incurred and all that’s left is passively wait and wonder if the results will eventually justify the expenditure (fire and forget). We are talking about a situation when it is still possible to  increase the investment (incur more costs) in the hope that the extra resources allocated to the undertaking will enable it to succeed. It is ideally illustrated by a simple but fascinating game called the dollar auction, first described in a scientific paper by Martin Shubik.

“A dollar bill is auctioned with these two rules:

1. (As in any auction) the dollar bill goes to the highest bidder, who pays whatever the high bid was. Each new bid has to be higher than the current high bid, and the game ends when there is no new bid within a specified time limit.

2. (Unlike at Sotheby’s!) the second-highest bidder also has to pay the amount of his last bid – and gets nothing in return. You really don’t want to be the second-highest bidder.

Shubik wrote, “A large crowd is desirable. Furthermore, experience has indicated that the best time is during a party when spirits are high and the propensity to calculate does not settle in until at least two bids have been made.”

Shubik’s two rules swiftly lead to madness. “Do I hear 10 cents?” asks the auctioneer – “5 cents?”

Well, it’s a dollar bill, and anyone can have it for a penny. So someone says 1 cent. The auctioneer accepts the bid. Now anyone can have the dollar bill for 2 cents. That’s still better than the rate Chase Manhattan gives you, so someone says 2 cents. It would be crazy not to.

The second bid puts the first bidder in the uncomfortable position of being the second-highest bidder. Should the bidding stop now, he would be charged 1 cent for nothing. So this person has particular reason to make a new bid – “3 cents.” And so on

Maybe you’re way ahead of me. You might think that the bill will finally go for the full price of $1.00 – a sad comment on greed, that no one got a bargain. If so, you’d be way too optimistic.

Eventually someone does bid $1.00. That leaves someone else with a second-highest bid of 99 cents or less. If the bidding stops at $1.00, the underbidder is in the hole for as much as 99 cents. So this person has incentive to bid $1.01 for the dollar bill. Provided he wins, he would be out only a penny (for paying $1.01 for a dollar bill). That’s better than losing 99 cents.

That leads the $1.00 bidder to top that bid. Shubik wrote, “There is a pause and hesitation in the group as the bid goes through the one dollar barrier. From then on, there is a duel with bursts of speed until tension builds, bidding then slows and finally peters out.”

No matter what the stage of the bidding, the second-highest bidder can improve his position by almost a dollar by barely topping the current high bid. Yet the predicament of the second-highest bidder gets worse and worse! This peculiar game leads to a bad case of buyer’s remorse. The highest bidder pays far more than a dollar for a dollar, and the second-highest bidder pays far more than a dollar for nothing.

Computer scientist Marvin Minsky learned of the game and popularized it at MIT. Shubik reported: “Experience with the game has shown that it is possible to ‘sell’ a dollar bill for considerably more than a dollar. A total of payments between three and five dollars is not uncommon.” Possibly W. C. Fields said it best: “If at first you don’t succeed, try, try again. Then quit. No use being a damn fool about it.”

Shubik’s dollar auction demonstrates the difficulty of using von Neumann and Morgenstern’s game theory in certain situations. The dollar auction game is conceptually simple and contains no surprise features or hidden information. It ought to be a “textbook case” of game theory.

It ought to be a profitable game, too. The game dangles a potential profit of up to a dollar in front of the bidders, and that profit is no illusion. Besides, no one is forced to make a bid. Surely a rational player can’t lose. The players who bid up a dollar to many times its value must be acting “irrationally.”

It is more difficult to decide where they go wrong. Maybe the problem is that there is no obvious place to draw the line between a rational bid and an irrational one. Shubik wrote of the dollar auction that “a game theory analysis alone will probably never be adequate to explain such a process.”

William Poundstone, Prisoner’s Dilemma, Doubleday, NY 1992, pp. 280-282 via

As can be seen, the dollar auction is a trap, and the only way to succeed is in this game is not to take part in it in the first place, collude with the other high bidder (if collusion is technically possible and ethically acceptable, which is rarely the case), or to be the auctioneer oneself. As argued above, in real life, falling into this kind of trap is sometimes unavoidable, even if no obvious mistakes had been made in the decision-making process. The challenge is therefore not to avoid such situations altogether (as it would mean avoiding decision-taking altogether), but to learn to deal with them properly, and this is an opportunity for a high caliber leader to shine.

Sadly, a lot of leaders fail to go the right path which is to admit defeat, withdraw from the game, and come to terms with the losses. Instead, they put their egos before the best interests of their organizations and elect the ostrich strategy.

Głowa w piasek Fotografia Art Photography Fotoklimat

Such an approach may defer the inevitable but only at the expense of greater losses being suffered in the future, just like in the dollar auction. A classic example is the Vietnam war. The first fatal error of the US leaders was the political decision to send American troops to fight a war there in the first place. Let’s leave it to military historians to ascertain whether the error could and should have been avoided. Regardless of the answer, as the conflict escalated, it became painfully clear that the initial US involvement was not enough to win the war. Therefore, more and more troops were being sent to Vietnam to gain an advantage over the enemy and to turn the tide in the United States’ favor. At the same time, more and more US soldiers were being sent back to America in plastic body bags. The number of US casualties grew from just over 200 in 1964 to almost 2,000 in 1965, and then, on average, doubled each year during the three consecutive years. Unfortunately for America (not to mention Vietnam, who lost not tens but hundreds of thousands in casualties), its leaders persisted in this lose-lose strategy, refusing to admit that the war cannot be won. As the cost of the ‘game’ (both expressed in human lives and US dollars) increased, it became more and more politically difficult to withdraw as it would mean admitting that the young men died for nothing, which would mean a huge loss of face for war supporters. As a result, the war was lost anyway, only the losses, which could have been kept low if the right decisions had been taken in time, grew to a disastrous size.

To conclude, leadership is very much about making decisions and about delegating the decision-making right to others. Given the uncertain nature of reality and all kinds of risks which can never be fully eliminated, some of the decisions are guaranteed to produce bad results. It is essential that these failures are recognized early. If there is a real (rather than an imaginary) chance for success, it could make sense to uphold the original decision, i. e., invest more in the undertaking. If not – it is crucial to write it off when the losses are still small. This should be followed by a fact-based analysis aimed at finding the root causes of the failure and not a scapegoat. It is a good leadership practice not only to take full accountability, especially when things go wrong, but also to let others see that this is not the end of the world. Admitting that what began as a promising project ended up as a sunk cost may not be fun, but it is part of the leader’s job (remaining in denial in order to protect one’s ego is not). Most of the time, such an attitude will not only gain a leader credibility and respect (thus helping the bruised ego to recover quickly), but it will also encourage similar behavior among other decision-makers, which, in turn, will be reflected in the company’s profit & loss account by limiting potentially multi-million losses to peanuts. A genuine leader sometimes has to take it on the chin (think no pain, no gain). Arguably, it is not only a rational and ethical approach, but also one that’s likely to be rewarded.

Competition: Muhammad Ali hits Ron Lyle, left, with a hard right to the chin during the title bout in Las Vegas, Nevada, in 1975. Lyle died last Saturday

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