Emergic: Rajesh Jain's Blog

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Splitting a Shared Cab Ride

December 18th, 2005 · No Comments

WSJ presents a number of options to the following: “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?”

One solution: “Harvard University economist David Laibson suggests looking to Prof. Nash’s work for a solution. The Nash bargaining strategy — an approach based on game theory in which each cab passenger is seen as a party to the deal and is negotiating his best outcome — would have the passengers split the savings equally, so that A, B and C each gets $2 knocked off his bill. Why share the savings equally? Think of the shared cab ride as a contract being struck to yield savings: Any party could walk away from the deal and kill it, so each should share equally in the fruits of the deal. With the numbers I’ve chosen, this method yields the highly unlikely scenario that B pays $3, C pays $7 and A makes a profit of $1 for his troubles….Prof. Laibson suggests eliminating that troublesome possibility by adding an exception: If splitting the savings equally means one passenger is getting paid, give him a freebie and split up the rest of the savings equally. So A would get a free ride, B pays $2.50, and C pays $6.50.”

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