# Monthly Archives: December 2005

## The microeconomics of “Deal or No Deal”

Every economics nerd in the country had to be ecstatic when they tuned in to watch NBC’s “Deal or No Deal”. After watching the show for all of two minutes I turned to my wife and exclaimed something about it being a great example of microeconomic theory. She rolled her eyes. I programmed the TiVo.

The show is a game show format. A contestant chooses one of 26 different briefcases. Each briefcase contains a dollar amount between \$.01 and \$1,000,000. The contestant then participates in a series of rounds where the amounts inside the other briefcases are revealed. After each round, the “banker” offers the contestant a dollar amount to buy the briefcase back. The contestant then has to decide whether to continue to the next round or take the offered amount of money. If the numbers revealed in the next round are high numbers, the banker’s offer will decrease. If, however, the opposite occurs and lower numbers are revealed the briefcase is assumed to have a higher value and the banker will increase their offer.

You do not have to be an economics nerd like myself to enjoy the show, but it certainly makes the game more entertaining. Take, for example, Tuesday night’s first contestant. He was down to six numbers left: \$300. 700. 10,000. 300,000. 400,000. 500,000. The offer from the banker was \$99,000. Would you take the offer?

Using microeconomic theory, one could calculate that the expected value was roughly \$201,841. Whether or not he should take the amount depends on his utility. Theory tells us that we cannot calculate utility in everyday life, but in this case we can get an idea. If he chose to continue then we could safely assume that his expected utility of \$201,841 is greater than his utility of \$99,000.

The contestant showed rejected the offer and continued to reject other offers. When there were only four numbers remaining the contestant was offered \$240,000. The numbers remaining were: 10,000. 300,000. 400,000. 500,000. The expected value in this case was \$302,500. He continued and his fiancé screamed, “I cannot believe he’s going for it.” I on the other hand could believe it. It was a simple matter of utility. The next box was revealed to be \$500,000. Now the expected value was approximately \$236,666. The offer was now reduced to \$189,000. He accepted this offer.

So what do these results tell us about the contestant? This tells us that this particular contestant has a Friedman-Savage utility function. For non-nerds this means that he is risk seeking with respect to a large gamble and risk averse with respect to a small gamble. In this case, he was willing to give up \$99,000 because his expected value was more than twice that amount. However, when offered \$189,000 he was unwilling to continue because the expected value was not much higher.

“Deal or No Deal” is a prime example of microeconomic theory at work. If the show lasts long enough (and I hope that it does), it could be a useful tool for more expansive studies of the relationship between risk and utility. In the meantime, I will continue watching the show while my wife rolls her eyes. Oh, and for those of you wondering, the contestant’s briefcase contained the value of \$10,000.