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Thursday, December 15, 2005

Three Economists Get Into A Cab

This sounds like the beginning of a joke:
Three economists get into a cab. They're each getting off at different places along the route. How should they split the bill?

It's not a joke but an everyday numbers dilemma, and it highlights some important economic principles. I asked several economists to solve the problem, and they came up with some unique approaches. One called on the work of game-theory pioneer John Nash (the inspiration for "A Beautiful Mind") to divide up the bill. Another referenced the ancient Jewish legal text, the Talmud.

It's actually the beginning of a piece in the Wall Street Journal by Carl Bialik (The Numbers Guy). It's an interesting question, since there's a savings to be had by cooperating (the cost of sharing the cab is less than the total costs the three economists would pay if they took separatecabs. Here's the question:

For the sake of this column, we'll stick with the case of a cab running on a meter, and we'll assume that all of the passengers are traveling in the same general direction -- some just live farther from the starting point than others. It's easy to apply the sharing schemes we devise to more complex scenarios.

Let's say that passenger A's usual fare would be $1, passenger B's is $5 and passenger C's is $9. If all three share a cab (and assuming A and B are allowed to hop out on the way to C's destination, without incurring any special fees), the total bill would be $9 -- rather than the $15 they'd have to pay, total, to ride alone. How should they divide up the cost of the shared $9 ride? Or, put another way, how do they share the $6 of total savings?

Before you check out the proposed solutions, what do you think is the fairest solution. Then read the article here (note: online subscription required).

As an aside, Yale's Barry Nalebuff (one of the economists mentioned in the article) has an excellent non-technical (i.e. almost math-free) book with Arvinash Dixit on game theory called Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life. If you'd like to get a taste of what game theory's all about, it's as good an introduction as you're going to find.







WSJ.com - The Numbers Guy

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