Monday, December 12

Game theory of The Price is Right: Part 1

In an attempt to improve my French, I have discovered a newfound appreciation for The Price is Right. Having watched the show as a kid but forgotten about it in recent years, I was excited when a Qu├ębecois version of Bob Barker's classic game show was launched this fall. I have found that it is an enjoyable way to keep up my French vocabulary.

It's also the first time that I've watched the show on a regular basis since studying economics, which can make for a surprisingly frustrating experience. For instance, on Cliffhangers (the "yodelling game"), I find myself cringing when contestants make their final bid.

The game works as follows: the contestant must guess, one at a time, the prices for three items. After a guess is made, the true price is revealed, and for each dollar that the contestant's guess is off, the yodeller moves one notch up the mountain. If the guesses are off by a combined $26 or more, the contestant loses. Otherwise, they win a bigger prize (in the case of the video above, a trip to New Orleans).

There is one other rule that is made explicit in the French game: the items are ordered from lowest to highest price. This should make the last bid straightforward in most circumstances. In the case above, for example, the second item was worth $30. This means that it would be stupid to guess less than $31 for the third item. But in the case above, the yodeller can still move 22 notches up the mountain without falling off. Therefore, it would be stupid to bid less than $53. With a $53 guess, the contestant will win if the third prize is $31 (the minimum amount it could possibly be). They will also win if the third item is $75 or less.

It could be smart to bid more than $53 — if they believe the price of the item is particularly high — but it is never smart to bid less than $53. The proof: Let's say I bid $50. I'll still win the item if it's $31 — the least it could be — but if it's $75, I'd lose this time. I'd only win if the item is less than $72.

Yet every time I watch the French version, the contestants, like the woman in the video, bid less than the number of remaining notches + value of the second item + 1. Which is suboptimal. Which makes the economist in me very angry.