It’s been a while since

It’s been a while since Beautiful Mind came out, but I recently came across this well-written piece by someone who was actually in the math department at Princeton and saw John Nash slinking around (before the movie made him more famous than the Nobel already had). The author, Daniel Grech, does a good job of capturing the essence of what “Nash equilibrium” means.

Read What Nash’s ‘Beautiful Mind’ Really Accomplished for the details, but here’s the key example the Grech provides about how market equilibrium is not always efficient.

Two gas stations are being built in a small town made up of a single, one-mile long Main Street. Town planners agree that the gas stations should be placed at one-quarter and three-quarter mile marks, so that no one in town has to drive more than a quarter mile to fill up. And since residents are distributed evenly along Main Street, both stations would share exactly half the business in town.

But try explaining that to the station owners. The owner who should build at the one-quarter mile mark knows people at his end of town will never go to the competing station because it’s too far away. So he’d want to build closer to the center of town to dip into his competitor’s mid-town market. Of course, the other owner is equally wily and he too edges his station closer to the center of town. Game theory tells us—and an astute business sense dictates—that the two gas stations will both end up on the same corner in the exact center of Main Street.