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Game Shows
With all the research about financial markets, where the stakes are surely high, plus the football paper, we were clearly making headway against the critique that the behavioral anomalies observed in the lab would not be replicated in the so-called real world. But it was too early to declare victory. Myths are hard to kill. Furthermore, there was one limitation to these findings: for the most part, they pertained to market prices rather than specific individual behavior. Yes, the price of draft picks was off, but it was not possible to pin down the specific behavioral cause. Indeed, the fact that many behavioral phenomena, from overconfidence to the winner’s curse, predicted that early picks would be overvalued made it impossible to say which bit of misbehaving was producing the mispricing. And although the behavior of cab drivers and individual investors had plausible explanations based on prospect theory, it was impossible to rule out other explanations consistent with expected utility maximization, perhaps associated with biased beliefs. Economists are really good at inventing rational explanations for behavior, no matter how dumb that behavior appears to be.
The highly stylized questions that Kahneman and Tversky had used to build prospect theory were designed to eliminate all possible ambiguities. When a subject is asked: “Would you rather have $300 for sure or a 50-50 chance at winning $1,000 or losing $400?” the probability of winning is known to be precisely 50% and the problem is so simple that there can be no other confounding factors contributing to a subject’s answers. Danny and Amos “solved” the high-stakes problem by making the questions hypothetical, so subjects imagined that they were making non-trivial choices, but no one had the budget to make such choices real. Even the researchers using the strategy of going to a poor country in order to raise the stakes rarely used stakes that were for more than a few months’ income; important, but not the kinds of stakes that arise in buying a house, choosing a career, or getting married. The search for a way to replicate Amos-and-Danny-type questions at truly high stakes was still unfulfilled when, in 2005, I happened to find an answer in the Netherlands.
The occasion was the award to me of an honorary degree at Erasmus University in Rotterdam. Aside from the honor, the highlight of the visit was a meeting with three economists: Thierry Post, a tenured finance professor, Martijn van den Assem, a new assistant professor, and Guido Baltussen, a graduate student. They had a project that studied the decisions made on a Dutch television game show. I was intrigued by their project, and was excited about their preliminary findings supporting the existence of a house money effect at very high stakes. (Recall that the house money effect, introduced in chapter 10, says that people are more willing to take chances when they think they are ahead in the game.) In this context, contestants faced decisions involving hundreds of thousands of dollars. Perhaps the myth that behavioral findings wilt in the face of high stakes could be finally put to rest. They asked me if I would like to join the team and work with them on the project and I agreed.*
If someone had asked me to design a game in order to test prospect theory and mental accounting, I could not have done better than this one. The show was created by a company called Endemol, and although the original version appeared on Dutch television, the show soon spread around the world. We used data from the Dutch, German, and United States versions of the show. The name of the show in Dutch was Miljoenenjacht (“Chasing Millions”) but in English the show was called Deal or No Deal.
The rules were roughly the same in all versions of the show, but I will describe the original Dutch version. A contestant is shown a board (see figure 23) showing twenty-six different amounts of money varying from €0.01 to €5,000,000. Yes, you read that correctly, five million euros, or more than six million U.S. dollars. The average contestant won over €225,000. There are twenty-six briefcases, each containing a card displaying one of those amounts of money. The contestant chooses one of those briefcases without opening it and may, if he wishes, keep that until the end of the show and receive the amount of money it contains.
Having chosen his own briefcase, the contents of which remain secret, the contestant must then open six other briefcases, revealing the amounts of money each contains. As each case is opened, that amount of money is removed from the board of possible payoffs, as shown in the figure. The contestant is then offered a choice. He can have a certain amount of money, referred to as the “bank offer,” shown at the top of the board, or he can continue to play by opening more cases. When faced with the choice between the bank offer and continuing to play, the contestant has to say “Deal” or “No deal,” at least in the English version of the show. If the contestant chooses to continue (“No deal”), he will have to open additional cases on each round. There are a maximum of nine rounds, and the number of cases to be opened on the remaining rounds are five, four, three, two, one, one, one, and one.
FIGURE 23
The size of the bank offer depends on the remaining prize money left on the board and the stage of the game. To keep players playing and make the show more entertaining, the bank offers in the early rounds of the game are a small proportion of the expected value of the remaining prizes, where the “expected value” is the average of all the remaining amounts. When the game begins, before any cases are opened, the expected value is nearly €400,000. In the first round, the offers are about 10% of expected value, but the offers can reach or even exceed the expected value in the later rounds. By round six, the bank offers average of about three-quarters of the expected value and contestants are facing difficult, high-stakes decisions. Although the fact that the bank offer rises as a percentage of expected value as the game progresses gives players an incentive to keep going, they do run the risk that they will be unlucky in their choice of which cases to open. When cases with large monetary prizes are opened, the expected value drops and so does the bank offer.
Our primary goal in the paper was to use these high-stakes decisions to compare standard expected utility theory to prospect theory,† and beyond that, to consider the role of “path dependence.” Does the way the game has played out influence the choices people make? Economic theory says that it shouldn’t. The only thing that should matter is the choice the contestant is now facing, not the good or bad luck that occurred along the way. The path is a SIF.
One seemingly mundane finding is of significant importance in evaluating the competing theories. Players are only “moderately risk averse”—they are not extremely risk averse. Many players reject cash offers of 70% of expected value, and thus commit themselves to continuing to take chances, even when hundreds of thousands of euros are on the line. This finding is relevant to the literature on the equity premium puzzle. Some economists pointed out that there would not be a puzzle if investors were very highly risk averse. The results from the game show gave no support to this hypothesis. One simple illustration of this fact is that no player in the Dutch show stopped playing before the fourth round of the game although hundreds of thousands of euros were on the line. A player with a level of risk aversion high enough to explain the equity premium puzzle risk would never make it that far into the game.
Of more interest is the role of path dependence. In my paper with Eric Johnson that had been motivated by my colleague’s poker-playing proclivities, we found two situations that induce people to be less risk averse than normal, in fact, actively risk-seeking. The first is when they are ahead in the game and “playing with the house money.” The other is when they are behind in the game and have a chance to break even. The contestants on Deal or No Deal displayed the same tendencies, and for huge stakes.
To see what can happen to someone who considers himself “behind” in the game, consider the plight of poor Frank, a contestant on the Dutch show. The six cases Frank chose to open in the first round were mostly lucky ones, with only one of the cases having a large number, and his expected value was over €380,000. But in the second round he was very unlucky, picking four of the large prizes. His expected value plumme
ted to around €64,000, and the bank was offering him only €8,000. Frank was very much in the mood of someone who had just lost a lot of money. Frank pressed on, his luck improved, and he reached an interesting decision at stage six. The remaining prizes were €0.50, €10, €20, €10,000 and €500,000, which average out to €102,006. He was offered €75,000, fully 74% of expected value. What would you do?
Notice that his distribution of prizes is highly skewed. If the next case he opens contains the half million prize, he will have lost any chance of a prize more than €10,000. Frank, still determined to win the big money he had been expecting, said, “No deal.” Unfortunately, he next picked the half million case, dropping his expected prize money to €2,508. Despondent, Frank persisted to the end. In the last round there were two amounts left: €10 and €10,000. The banker, feeling sorry for Frank, offered him €6,000, 120% of expected value. Frank again said, “No deal.” He left the show with 10 euros.
The other extreme is illustrated by Susanne, who appeared on the less lucrative German version of the show, where the average contestant won “only” €20,602, and the largest prize was €250,000. Susanne had a lucky run of picks, and in the last round had only €100,000 and €150,000 as the remaining prizes, two of the three largest amounts. She received a bank offer of €125,000, exactly the expected value, yet she said, “No deal,” undoubtedly thinking that she was only risking €25,000 of “house money.” Lucky Suzanne walked away with €150,000.
Frank and Susanne’s decisions illustrate the more formal findings of the paper, which show strong support for path dependence. Contestants clearly reacted not just to the gambles they were facing, but also to the gains and losses along the way. The same behavior I had first observed with my poker buddies at Cornell, and then tested for tens of dollars with Eric Johnson, still arises when the stakes are raised to hundreds of thousands of euros.
One concern with using the data from television game shows to study behavior is that people might act differently when they are in public than they would in private. Fortunately, Guido, Martijn, and Dennie van Dolder, then a graduate student, ran an experiment to measure the difference between public and private decisions.
The first stage of the experiment aimed to replicate the results of the televised games with students in front of an audience. They would simulate the television show as closely as possible, with a live master of ceremonies, a crowded auditorium, and cheering fans. The one thing that could not be replicated, of course, was the size of the payoffs. Payoffs were reduced by a factor of either 1,000 (large stakes), or 10,000 (small stakes). The biggest payoffs were €500 and €5,000 in the small- and large-stakes versions respectively. One interesting finding from these experiments is that the choices made were not very different from those in the televised version. As expected, at lower stakes, students were a bit less risk averse overall, but not dramatically so. Also, the pattern of path dependence reemerged, with both big winners and big losers becoming more risk-seeking.
The study went on to compare these experiments with others that had students make private decisions on a computer in the laboratory. The way these experiments were designed, a student in the lab would face exactly the same set of choices and real stakes that occurred in games played in front of a live audience. Time for a thought experiment: in which situation will the students undertake more risk, when choosing by themselves or in front of the crowd?
The results were a surprise to me. I thought that choosing in front of the crowd would induce students to take more risks, but in fact the opposite happened. The students were more risk averse in front of the crowd. Otherwise, the results were quite similar, which is comforting, since my career as a student of game shows was just getting started.
Another domain that attracted the “what if you raise the stakes?” complaint was so-called “other-regarding” behavior, such as the Ultimatum Game and Dictator Game. Here again, researchers had been able to raise the stakes to a few months’ income, but some still wondered what would happen if “real money” was at stake. Sometime after our Deal or No Deal paper appeared, Martijn got in touch with me about a project he was doing with Dennie van Dolder. Endemol had come up with another game show that begged to be analyzed from a behavioral perspective. The show is called, of all things, Golden Balls.
The finale of each episode is what captured our attention. The show starts with four contestants, but in preliminary rounds two of them are eliminated, with the two survivors left to play one final game for stakes that can be quite high. At this final stage they play a version of the most famous game in all of game theory: the Prisoner’s Dilemma. Recall the basic setup: Two players have to decide whether to cooperate or defect. The selfish rational strategy in a game that will only be played once is for both players to defect, but if they can somehow both cooperate, they do much better. Contrary to the standard theory, in low-stakes experiments of the Prisoner’s Dilemma, about 40–50% of people cooperate. What would happen if we raise the stakes? Data from Golden Balls allowed us to find an answer.
On the show, the two finalists have accumulated a pot of money and have to make a decision that determines how this prize will be divided; they can choose to “split” or “steal.” If both players choose to split, they each get half the pot. If one player says “split” and the other says “steal,” the one who says “steal” gets everything and the other gets nothing. And if both players choose to steal, they both get nothing. The stakes are high enough to make even the most stubborn of economists concede that they are substantial. The average jackpot is over $20,000, and one team played for about $175,000.
The show ran for three years in Britain, and the producers were kind enough to give us recordings of nearly all the shows. We ended up with a sample of 287 pairs of players to study. Our first question of interest was whether cooperation rates would fall at these substantial stakes. The answer, shown in figure 24, is both yes and no.
FIGURE 24
The figure shows the percentage of players who cooperate for various categories of stakes, from small to large. As many had predicted, cooperation rates fall as the stakes rise. But a celebration by defenders of traditional economics models would be premature. The cooperation rates do fall, but they fall to about the same level observed in laboratory experiments played hypothetically or for small amounts of money, namely 40–50%. In other words, there is no evidence to suggest that the high cooperation rates in these low-stakes conditions are unrepresentative of what would happen if the stakes went up.
Cooperation rates fall as the stakes rise only because when the stakes were unusually low by the standards of this show, cooperation rates were exceptionally high. My coauthors and I have a conjecture for why this happens that we call the “big peanuts” hypothesis. The idea is that a certain amount of money can seem small or large depending on the context. Recall from the List that people were willing to drive across town to save $10 on a small purchase but not a big one. Ten dollars in the context of buying a new television seems like “peanuts,” or not enough to worry about. We think the same thing happens on this show. Remember that the average prize pool in this game is about $20,000, so if a pair of contestants find themselves in a final where the pot is just $500, it feels like they are playing for peanuts. If they are playing for peanuts, why not be nice, especially on national television? Of course, $500 would be considered an extraordinarily large prize to be divided in the context of a laboratory experiment.
There is evidence for the same “big peanuts” phenomenon in our Deal or No Deal data. Remember unlucky Frank who was, in the last round, offered the choice between a sure €6,000 versus a 50-50 chance of getting either €10,000 or €10, and he chose to gamble. We suspect that after beginning the game with an expected payoff of nearly €400,000 and having been offered as much as €75,000 in past rounds, Frank thought he was down to playing for peanuts and decided to go for it.
We investigated one other aspect of the behavior displayed on Golden Ball
s: could we predict who would split and who would steal? We analyzed a host of demographic variables, but the only significant finding is that young men are distinctly less likely to split. Never trust a man under thirty.
We also analyzed the speeches each player makes before the big decision. Not surprisingly, the speeches all have the same flavor: “I am not the sort of person who would steal, and I hope you are not one of those evil types either.” This is an example of what game theorists call “cheap talk.” In the absence of a penalty for lying, everyone promises to be nice. However, there turns out to be one reliable signal in all this noise. If someone makes an explicit promise to split, she is 30 percentage points more likely to do so. (An example of such a statement: “I promise you I am going to split it, 120%.”) This reflects a general tendency. People are more willing to lie by omission than commission. If I am selling you a used car, I do not feel obligated to mention that the car is burning a lot of oil, but if you ask me explicitly: “Does this car burn a lot of oil?” you are likely to wangle an admission from me that yes, there has been a small problem along those lines. To get at the truth, it helps to ask specific questions.
We had students coding everything that happened on each episode, and I only watched a dozen or so to get a feel for how the game was played. So, it was only after a particular episode went viral on the Internet that I realized Golden Balls may well have had one of the best moments ever recorded in a television game show—admittedly not a category with a lot of competition. The players in this game were Nick and Ibrahim, and the star of the game was Nick. It seems that Nick has made a nice sideline career as a game show contestant, appearing on over thirty different shows. He put all his creativity to use on this one.
Misbehaving: The Making of Behavioral Economics Page 32
