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For example, if 100 of us are each choosing one of two routes for our morning commute, you probably don’t care of them.
Economists could use such arguments to justify why Nash equilibrium might be attainable for particular games.
In 1950, John Nash — the mathematician later featured in the book and film “A Beautiful Mind” — wrote a two-page paper that transformed the theory of economics.
The new paper shows, however, that this same limitation holds even if the players are willing to make do with an approximate Nash equilibrium — an important finding when it comes to real-world applications, in which an outcome that’s close to a Nash equilibrium is often good enough.“If you’re trying to figure out if your game will easily find an equilibrium,” said Noam Nisan, a computer scientist at the Hebrew University, “it’s on you to provide the argument why it would be.” In some simple games, it is easy to spot Nash equilibria.For example, if I prefer Chinese food and you prefer Italian, but our strongest preference is to dine together, two obvious equilibria are for both of us to go to the Chinese restaurant or both of us to go to the Italian restaurant.But the new result implies that such justifications must be made on a case-by-case basis; there’s no killer argument that will cover all games all the time.What’s more, even though many games that have evolved along with civilization may be amenable to such simplifications, the Internet era is giving rise to all kinds of new many-player games, from dating sites to online stock trading.
When players are at equilibrium, no one has a reason to stray.