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Thursday, January 12, 2006
Game Theory
Why game shows have economists glued to their TV sets... from today's Journal, in the comments.
2 comments:
Anonymous
said...
For Researchers, Players Shed Light on Decision Making; Mr. Johnson's 'Gutsy' Move
By CHARLES FORELLE Staff Reporter of THE WALL STREET JOURNAL January 12, 2006; Page A1
Daryl Johnson, a 27-year-old actor and freelance Web designer -- "which means I don't have a job" -- was shifting his weight nervously on the TV game show "Deal or No Deal."
After disappointing rounds that dashed Mr. Johnson's hopes of walking away a millionaire, the host, Howie Mandel, offered him $37,000 to quit. Mr. Johnson still had a one-in-five shot at winning a briefcase with $200,000 hidden inside. So he turned down the $37,000.
Later, with only a one-in-three chance left of winding up with the $200,000, Mr. Johnson was offered $67,000 to give up. He rubbed his hands. He drummed his fingers on his chest. He shook his head no. The audience hooted.
"You're very gutsy," Mr. Mandel said.
To Thierry Post, a professor of finance at Erasmus University in Rotterdam, the Netherlands, Mr. Johnson is also an invaluable subject in economics research. "His risk appetite is really abnormal," the professor says of Mr. Johnson. More precisely, he calculates, Mr. Johnson displayed a "relative-risk aversion" measure of 0.006 -- unusually, almost completely, indifferent to financial risk.
Mr. Post is part of a small, intense cadre of economists who study game shows in a variation on "game theory," seeking to explain the situational choices contestants make, and the clues those choices may hold for economic behavior in everyday life.
In a 2002 paper notable in game-show delving, two economists calculated the "unique subgame-perfect Nash equilibrium" -- roughly, the best way to play -- in a segment of "The Price Is Right." They found that contestants frequently deviated from it, acting too conservatively when worried about being eliminated.
Other shows that have been studied include "Who Wants to Be a Millionaire" and "Jeopardy!" But "Deal or No Deal" has created particular excitement, in part because it involves no skill whatsoever. That reduces the variables when comparing subjects.
"There is no doubt that these are real people making real choices for high stakes, and we rarely get to observe such pure decisions," says Richard Thaler, a leading behavioral economist at the University of Chicago Graduate School of Business.
Economists aren't the only ones captivated by "Deal or No Deal," which originated in Holland and has been broadcast in 38 countries. The U.S. version, broadcast several times on NBC last month, will return to the air after the Olympics.
Mr. Post is studying the show to see whether it might help explain why people make irrationally risky economic decisions. He and his colleagues have recorded dozens of episodes. They've traded online with TV-show collectors around the world and have even hired Turkish-speaking students to transcribe data from Turkey's version of the show.
How risk affects financial behavior bears on such weighty matters as deciding which assets to put in an investment portfolio and how much governments should spend on social safety nets. But actual data are rare. Giving away millions of dollars to subjects of an experiment would be "hard to justify to the National Science Foundation," and others who pay for research, says Ian Walker, a professor at the University of Warwick in Coventry, England, who has studied "Who Wants to Be a Millionaire."
"Deal or No Deal" works like this: Twenty-six models each hold a briefcase that contains a sum of money -- varying from one cent to $1 million in the U.S. game. The contestant picks one briefcase as his own and then begins to open the other 25, each time, by process of elimination, revealing a little more about what his own case might hold. At the end, the contestant can also trade his briefcase for the last unopened one.
Suspense builds -- and the contestant's chance of hitting it big grows -- when small sums are eliminated and the $1 million or $750,000 cases remain unopened and winnable. Periodically, as cases are eliminated, an ominously shrouded "banker" offers a deal conveyed to the contestant by Mr. Mandel. The proposal is: Stop playing now and take the money offered.
What interests Mr. Post is how contestants respond to these offers, which are related to which dollar sums remain winnable. If the $1 million and $500,000 briefcases are left, for instance, the offer will be far higher than if they aren't.
This can create anguishing scenarios. What to do if the last two briefcases hold $1 million and $10, and the banker offers $450,000? The contestant has a 50-50 chance at a million. Probability theory says his "expected value" is the average of the two unopened briefcases, or $500,005. Classical economic theory says that people with relatively small net worth, likely never again to see a $450,000 check, would take it. Behavioral economists say that isn't always the case.
In this game, there's no trivia. No vowels to buy, no wheels to spin. Decisions involve only dollars, and contestants have just one choice at each juncture: Is it a deal or no deal? "You are a complete moron" if you don't understand the show's simple pattern, says Mr. Post, who is head of the finance department at the Erasmus School of Economics. It is thus "a dream come true for any behavioral economist."
Studying 53 episodes of the Dutch and Australian shows, Mr. Post finds that some contestants behave as the classical model predicts, locking up a sure payoff rather than risking it even with favorable odds. But others don't. The distinguishing factor, Mr. Post's data show: Players take more risks if they suffer setbacks early in the game, such as opening the million-dollar briefcase. That supports prospect theory, one of whose creators received a Nobel Prize in 2002. Prospect theory holds that people evaluate prospects for gains and losses from psychological reference points that may shift over time -- instead of seeking to maximize the "utility" they receive from money under an unvarying formula.
Zur Shapira, a psychologist at New York University's Stern School of Business, has been studying the qualifying rounds of the annual championship series in "Jeopardy!" He and a colleague, Elizabeth Boyle, calculated the best way to bet in Final Jeopardy, when players wager all, part or none of their winnings on one last question.
In the 1994 tournament of champions, contestant Tom Nichols had $8,200 going into the last round of his qualifying game and was in first place. (The winners of each qualifying game advance automatically to the next round, and the four highest scorers among the nonwinners also move on as wild cards.) Mr. Shapira's model holds that Mr. Nichols should have bet zero -- risking nothing for a solid shot at winning a wild-card slot for the next round -- instead of gambling for a win.
Balderdash, says Mr. Nichols, a political scientist who is now a professor of strategy at the Naval War College in Newport, R.I. "You'd have to be a boob" to assume the $8,200 "was gonna slide you into the final game," he writes in an email. Mr. Nichols bet $6,300, and was eliminated from the tournament when he named Alexander as the last king of the Hellenes. (It was Constantine II.) "This is so painful to remember," he says. "It is seared in my memory." Had he bet nothing, Mr. Nichols would have squeaked into the next round.
In "Deal or No Deal," Mr. Mandel says, the most surprising moment so far came when Karen Van, a self-described "sexy grandma," turned down $138,000 and ended up with a $25,000 prize. Ms. Van says her husband, who was in the studio audience, egged her on.
Mr. Johnson, who turned down eight deals, was faced with an ultimate choice between two briefcases. One contained $200,000, the other $50. The banker offered $99,000 to quit. "I'm no damn fool!" Mr. Johnson exclaimed. "Deal!" In an interview, he said he had, indeed, been gambling in the earlier rounds. Still, he wasn't going to go all the way.
2 comments:
For Researchers, Players Shed
Light on Decision Making;
Mr. Johnson's 'Gutsy' Move
By CHARLES FORELLE
Staff Reporter of THE WALL STREET JOURNAL
January 12, 2006; Page A1
Daryl Johnson, a 27-year-old actor and freelance Web designer -- "which means I don't have a job" -- was shifting his weight nervously on the TV game show "Deal or No Deal."
After disappointing rounds that dashed Mr. Johnson's hopes of walking away a millionaire, the host, Howie Mandel, offered him $37,000 to quit. Mr. Johnson still had a one-in-five shot at winning a briefcase with $200,000 hidden inside. So he turned down the $37,000.
Later, with only a one-in-three chance left of winding up with the $200,000, Mr. Johnson was offered $67,000 to give up. He rubbed his hands. He drummed his fingers on his chest. He shook his head no. The audience hooted.
"You're very gutsy," Mr. Mandel said.
To Thierry Post, a professor of finance at Erasmus University in Rotterdam, the Netherlands, Mr. Johnson is also an invaluable subject in economics research. "His risk appetite is really abnormal," the professor says of Mr. Johnson. More precisely, he calculates, Mr. Johnson displayed a "relative-risk aversion" measure of 0.006 -- unusually, almost completely, indifferent to financial risk.
Mr. Post is part of a small, intense cadre of economists who study game shows in a variation on "game theory," seeking to explain the situational choices contestants make, and the clues those choices may hold for economic behavior in everyday life.
In a 2002 paper notable in game-show delving, two economists calculated the "unique subgame-perfect Nash equilibrium" -- roughly, the best way to play -- in a segment of "The Price Is Right." They found that contestants frequently deviated from it, acting too conservatively when worried about being eliminated.
Other shows that have been studied include "Who Wants to Be a Millionaire" and "Jeopardy!" But "Deal or No Deal" has created particular excitement, in part because it involves no skill whatsoever. That reduces the variables when comparing subjects.
"There is no doubt that these are real people making real choices for high stakes, and we rarely get to observe such pure decisions," says Richard Thaler, a leading behavioral economist at the University of Chicago Graduate School of Business.
Economists aren't the only ones captivated by "Deal or No Deal," which originated in Holland and has been broadcast in 38 countries. The U.S. version, broadcast several times on NBC last month, will return to the air after the Olympics.
Mr. Post is studying the show to see whether it might help explain why people make irrationally risky economic decisions. He and his colleagues have recorded dozens of episodes. They've traded online with TV-show collectors around the world and have even hired Turkish-speaking students to transcribe data from Turkey's version of the show.
How risk affects financial behavior bears on such weighty matters as deciding which assets to put in an investment portfolio and how much governments should spend on social safety nets. But actual data are rare. Giving away millions of dollars to subjects of an experiment would be "hard to justify to the National Science Foundation," and others who pay for research, says Ian Walker, a professor at the University of Warwick in Coventry, England, who has studied "Who Wants to Be a Millionaire."
"Deal or No Deal" works like this: Twenty-six models each hold a briefcase that contains a sum of money -- varying from one cent to $1 million in the U.S. game. The contestant picks one briefcase as his own and then begins to open the other 25, each time, by process of elimination, revealing a little more about what his own case might hold. At the end, the contestant can also trade his briefcase for the last unopened one.
Suspense builds -- and the contestant's chance of hitting it big grows -- when small sums are eliminated and the $1 million or $750,000 cases remain unopened and winnable. Periodically, as cases are eliminated, an ominously shrouded "banker" offers a deal conveyed to the contestant by Mr. Mandel. The proposal is: Stop playing now and take the money offered.
What interests Mr. Post is how contestants respond to these offers, which are related to which dollar sums remain winnable. If the $1 million and $500,000 briefcases are left, for instance, the offer will be far higher than if they aren't.
This can create anguishing scenarios. What to do if the last two briefcases hold $1 million and $10, and the banker offers $450,000? The contestant has a 50-50 chance at a million. Probability theory says his "expected value" is the average of the two unopened briefcases, or $500,005. Classical economic theory says that people with relatively small net worth, likely never again to see a $450,000 check, would take it. Behavioral economists say that isn't always the case.
In this game, there's no trivia. No vowels to buy, no wheels to spin. Decisions involve only dollars, and contestants have just one choice at each juncture: Is it a deal or no deal? "You are a complete moron" if you don't understand the show's simple pattern, says Mr. Post, who is head of the finance department at the Erasmus School of Economics. It is thus "a dream come true for any behavioral economist."
Studying 53 episodes of the Dutch and Australian shows, Mr. Post finds that some contestants behave as the classical model predicts, locking up a sure payoff rather than risking it even with favorable odds. But others don't. The distinguishing factor, Mr. Post's data show: Players take more risks if they suffer setbacks early in the game, such as opening the million-dollar briefcase. That supports prospect theory, one of whose creators received a Nobel Prize in 2002. Prospect theory holds that people evaluate prospects for gains and losses from psychological reference points that may shift over time -- instead of seeking to maximize the "utility" they receive from money under an unvarying formula.
Zur Shapira, a psychologist at New York University's Stern School of Business, has been studying the qualifying rounds of the annual championship series in "Jeopardy!" He and a colleague, Elizabeth Boyle, calculated the best way to bet in Final Jeopardy, when players wager all, part or none of their winnings on one last question.
In the 1994 tournament of champions, contestant Tom Nichols had $8,200 going into the last round of his qualifying game and was in first place. (The winners of each qualifying game advance automatically to the next round, and the four highest scorers among the nonwinners also move on as wild cards.) Mr. Shapira's model holds that Mr. Nichols should have bet zero -- risking nothing for a solid shot at winning a wild-card slot for the next round -- instead of gambling for a win.
Balderdash, says Mr. Nichols, a political scientist who is now a professor of strategy at the Naval War College in Newport, R.I. "You'd have to be a boob" to assume the $8,200 "was gonna slide you into the final game," he writes in an email. Mr. Nichols bet $6,300, and was eliminated from the tournament when he named Alexander as the last king of the Hellenes. (It was Constantine II.) "This is so painful to remember," he says. "It is seared in my memory." Had he bet nothing, Mr. Nichols would have squeaked into the next round.
In "Deal or No Deal," Mr. Mandel says, the most surprising moment so far came when Karen Van, a self-described "sexy grandma," turned down $138,000 and ended up with a $25,000 prize. Ms. Van says her husband, who was in the studio audience, egged her on.
Mr. Johnson, who turned down eight deals, was faced with an ultimate choice between two briefcases. One contained $200,000, the other $50. The banker offered $99,000 to quit. "I'm no damn fool!" Mr. Johnson exclaimed. "Deal!" In an interview, he said he had, indeed, been gambling in the earlier rounds. Still, he wasn't going to go all the way.
"Fifty dollars is a gas tank," he said.
That's really interesting. Thanks for posting it!
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