Priceless: The Myth of Fair Value (and How to Take Advantage of It) (19 page)

Amos Tversky told almost no one of the metastatic melanoma that was killing him. Deathly ill, he went into the office and worked up to three weeks before his death, on June 2, 1996. In the years since, behavioral decision theory has gained much ground with mainstream economists and even businesspeople. For the most part, the hair-splitting objections of Cohen and Gigerenzer and company have receded to near invisibility. Of late, a more pressing concern has been cheap prizes.

In the United States the ultimatum game is usually played with the sum of $10, an amount that won’t buy a movie ticket in Manhattan. Yet the psychologists and behavioral economists conducting such studies do so in the belief that their results have something to say about the wide world outside the lab. The ultimatum game responder (and implicitly all of us) is supposed to care a lot about how his share compares to the proposer’s and to be relatively insensitive to absolute dollar amounts.

Imagine a $10 million game, then. The proposer keeps $9 million for himself, leaving you a measly million. Do you pass up the million in order to teach him a $9 million lesson he’ll never forget?

Presumably not. Given that, proposers might demand a larger percentage . . . There has been a lot of speculation about how different a million-dollar ultimatum game would be. Some economists have argued that their kind of rationality kicks in after a certain number of zeros in the prize amount.

Elizabeth Hoffman, Kevin McCabe, and Vernon Smith got sick of hearing this talk. Their economist critics weren’t even necessarily thinking
of million-dollar prizes. Some were saying a $100 game would be different. Sure, people reject a dollar or two, but nobody in their right mind would turn down $10 or $20.

Hoffman and colleagues scraped together the money to run some $100 ultimatum games. That meant raising about $5,000 to run the game enough times to have statistical significance. In these experiments, done at the University of Arizona, there was no significant difference in behavior between the $100 games and the standard $10 games.

There was this note of drama. One proposer (illegally) scribbled a note to the responder on his offer form: “Don’t be a maryter [
sic
]; it is still the easiest $35 you’ve ever made.”

This proposer was offering a “cheap” $30 out of $100, and everyone got $5 just for showing up. The responder rejected the $30, adding the note: “
Greed
is driving this country to hell. Become a part of it and pay.”

In 2002, Dutch TV debuted a game show called
Miljoenenjacht
(
Chasing Millions
). It became a hit and led to local versions in more than sixty nations, from Mauritius to Argentina to the United States—where it’s called
Deal or No Deal.
The show poses dilemmas much like those studied by decision theorists, except that the sums of money are large and real. A 2008 article by Thierry Post, Martijn van den Assem, Guido Baltussen, and Richard Thaler notes that
Deal or No Deal
“almost appears to be designed to be an economics experiment rather than a TV show.”

Aside from the leggy models, there’s
no
TV show, just an economics experiment. In the U.S. version the game involves twenty-six female models, each carrying a briefcase that contains an unknown cash amount ranging from 1 cent to $1 million. The contestant begins by picking one of the twenty-six briefcases. He “owns” whatever is in the chosen briefcase. Rather than revealing the prize immediately, host Howie Mandel plays an extended cat-and-mouse game. He begins by revealing the prizes in a random group of briefcases that the contestant
didn’t
pick. By process of elimination, this provides indirect information about what might be in the chosen briefcase. All the prize amounts are posted on a scoreboard visible to contestants and the audience, and amounts are eliminated from the board as they are revealed.

A “banker” then offers the contestant a deal. Communicating by telephone
from a darkened office overlooking the stage, the banker offers to buy the contestant’s briefcase for a stated price. The player must therefore choose between the banker’s price and a gamble (keeping the briefcase and continuing with the game, with all its possible outcomes). The first banker offer is always small. If the contestant rejects it, more briefcases are opened, and the contestant comes to have a better picture of what is or isn’t in his briefcase. The banker makes further offers. Should the contestant keep rejecting offers, it ultimately comes down to a situation in which just two briefcases remain unopened. The banker names his final price. If the contestant refuses it, his briefcase is opened, and he gets whatever amount is inside.

Before any briefcases have been opened, the average of the twenty-six prizes in the standard American show is $131,477.54. That average changes as briefcases are opened. For instance, learning that an unchosen briefcase contains $1 million is bad news for the contestant, and it accordingly downsizes his prospects.

The only part of the show that isn’t completely transparent is how the banker computes his offers. In the early rounds, the offers are such a small fraction of the expectation that you’d be crazy to accept them. The offers grow more generous, relative to expectation, throughout the course of a game. The last offer is nearly the full expectation (in the U.S. game) or modestly more (in some other nations).

Thierry Post and colleagues got videotapes of several years’ worth of the Dutch, German, and U.S.
Deal or No Deal
games. They painstakingly analyzed every choice made by some 151 contestants in three countries. Consider Frank, a particularly luckless contestant on the Dutch show. Without batting an eye, Frank rejected banker offers as large as 75,000 euros, a comfortable year’s income. Frank ended up with 10 euros, enough for a good stiff drink.

Just before Frank opened his briefcase, there were two prizes in play, 10 and 10,000 euros. The banker offered 6,000 euros—more than the expected value of Frank’s briefcase, and a sweeter deal than is offered on the American show. Anybody’s mother, accountant, or fee-only financial advisor would have told Frank to take the deal. He wouldn’t take it; he was too intent on getting the 10,000 euros.

This behavior is hard to explain with any theory that assumes that choices depend on final wealth levels and nothing more. Anyone who
watches the whole episode will understand where poor Frank was coming from. He was reacting to all the bum luck that had befallen him prior to this final choice. Like every other contestant, Frank started out with high hopes and a high reference point. The top prize in the Dutch show is 5 million euros, far richer than the U.S. version. Frank saw his millionaire dreams dashed as the three biggest prizes were taken out of play in the first two rounds. Thereafter he felt like a loser. He did not see the banker’s offers as found money but as losses (relative to the fortunes he could have won). This made him willing to take risks.

The 1979 prospect theory article discusses dilemmas not unlike like Frank’s. Kahneman and Tversky report on this choice. In addition to whatever else you own, you have been given 1,000 Israeli pounds. You are now asked to choose between a 50 percent chance of an additional 1,000 pounds or what I’ll call a “banker offer” of 500. Eighty-four percent of Kahneman and Tversky’s subjects said “deal.” They preferred the sure thing to the gamble.

Then they rephrased the question and presented it to a different group. You’ve been given 2,000 Israeli pounds and must choose between a 50 percent chance of a 1,000
loss
or a “banker offer” that in this case is also a loss, of 500. Here 69 percent said no deal. They’d rather gamble than accept a sure loss.

The two versions of the problem are equivalent, going by what you walk away with. The second version just gives you an extra 1,000 up front and subtracts from that to arrive at the same two net outcomes of the first version. The wording of the second question encourages you to adopt the initial 2,000 pounds as a reference point. By framing the options as losses, it encourages risk taking.

Frank’s string of bad luck had the same effect. The banker’s final price registered as a loss—even though, under happier circumstances, Frank would have seen it as a windfall. This made him willing to play double or nothing.

Post’s team compared the performance of the expected utility model to prospect theory in predicting
Deal or No Deal
contestants’ decisions. They found that expected utility was correct 76 percent of the time, versus 85 percent for prospect theory. When serious money was at stake, prospect theory beat utility theory for predicting behavior.

Deal or No Deal
choices must be made on the spur of the moment. Post and colleagues conjecture, however, that the decisions made on the show may be about as carefully considered as those made in choosing mortgages or retirement portfolios. Like someone making a big financial move,
Deal or No Deal
contestants solicit advice from in-studio family and friends. Most contestants are undoubtedly fans of the show and probably plan their strategy long before their appearance. (A lot of people think mortgages and investments are
boring
and try not to think about them any more than they have to. Decisions are put off and put off, then finally made on the spur of the moment.)

The researchers also conducted two home versions of
Deal or No Deal
at Erasmus University, Rotterdam. They replicated the show “as closely as possible in a classroom” with a host (a popular lecturer) and a live audience, the better to “create the type of distress that contestants must experience in the TV studio.” They followed the script of televised games as closely as possible, using the same bank offers and random choices of which briefcases to open. This allowed comparison of the students’ behavior to the TV contestants’. The one difference was the size of the prizes. In one version, the prizes were 1/10,000 of those on the Dutch TV show, and in the other they were 1/1,000. The latter meant the top prize was 5,000 euros, and the average amount won was about 400 euros. That put this among the richest of all behavioral economics experiments.

If money is a magnitude scale, you’d expect the behavior to be about the same—and it was. The students in the cheaper experimental game played about the same as in the game where the stakes were ten times higher. Both groups’ behavior was similar to TV contestants playing for a thousand or ten thousand times more. Whether a banker’s price was judged “fair” was strongly influenced by a contestant’s history. Subjects who had been disappointed were, like Frank, less likely to accept a good price. Kahneman and Tversky could have been talking about
Deal or No Deal
when they wrote that “a person who has not made peace with his losses is likely to accept gambles that would be unacceptable to him otherwise.”

A Monty Python sketch concerns a mission to the planet Algon. Fifth world in the system of Aldebaran, Algon is suspiciously like 1972 Britain—except for its truly
astronomical
prices. As John Cleese has it,

Here an ordinary cup of drinking chocolate costs four million pounds, an immersion heater for the hot-water tank costs over six billion pounds, and a pair of split-crotch panties would be almost unobtainable . . . A new element for an electric kettle like this would cost as much as the entire gross national product of the United States of America from 1770 to the year 2000, and even then they wouldn’t be able to afford the small fixing ring which attaches it to the kettle.

Later in the bit, Michael Palin breaks in with the announcement that attachments for rotary mowers are “relatively inexpensive!—still in the region of nine to ten million pounds, but it does seem to indicate that Algon might be a very good planet for those with larger gardens.”

You might wonder how different Algon is from Earth, really. We are born onto the third world of Sol having no idea what things should cost. Perhaps we never learn. All we can do is take cues from the people around us. We act as if they’re sane and their prices make sense.

A Descartes of prices might deduce that the only thing we can truly know is relative values. In some deep sense, I can’t ever know whether 10 million pounds is a good price for a rotary mower attachment, but I can
know it’s cheaper than other prices. In a few short years, this daft view of prices, in which relative values matter and absolutes are almost meaningless, has become widely accepted due to some remarkable experiments. They show, you might say, that we all live on planet Algon.

Dan Ariely is another brilliant Israeli American who has thought deeply about the psychology of pricing. He traces some of his research to his first experience in a pricey chocolate store. Before him was an array of incredibly beautiful truffles with equally incredible prices. “I was thinking about what I wanted,” he said, “and I realized two things. One was that I quickly adapted to the level of prices. I didn’t think about how much chocolate costs in the supermarket.” The other thing was that “I was very susceptible—willing to take whatever suggested price the store was going to tell me was the right price to think about.”

Now a professor of behavioral economics at Duke University, Ariely is responsible for some of the most compelling demonstrations of how fluid prices are. One such experiment, done in collaboration with George Loewenstein and Drazen Prelec, was a silent auction of fancy chocolates, bottles of wine, and computer gear. The bidders, MBA candidates at MIT’s Sloan School, were asked to write down the last two digits of their social security numbers. Then each bidder had to indicate whether he would pay more or less than that two-digit number, in dollars, for each item being auctioned. Finally, bidders wrote how much they
were
willing to pay for it (an honest reserve price). Winning bidders paid money out of their own pockets and got to keep any items they won.