Nash equilibrium dating

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“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.By diving into the nitty-gritty of Nash’s proof, Babichenko and Rubinstein were able to show that in general, there’s no guaranteed method for players to find even an approximate Nash equilibrium unless they tell each other virtually everything about their respective preferences.And as the number of players in a game grows, the amount of time required for all this communication quickly becomes prohibitive.For example, in the 100-player restaurant game, there are 2.This communication bottleneck means that every possible method for adapting strategies from round to round is going to fail to guide players efficiently to a Nash equilibrium for at least some complex games (such as a 100-player restaurant game with complicated preferences).Babichenko and Rubinstein’s result does not imply that all, or even most, games will be subject to this limitation — only that some games will.

But Nash — who died in a car crash in 2015 — gave no recipe for how to calculate such an equilibrium.After all, in each round, the players learn only a bit of new information about each other: how happy they are with the single dinner arrangement that got played.So it will take on the order of 2 rounds before they know everything about one another’s values (by which time, presumably, the Chinese and Italian restaurants will have gone out of business).“They use these equilibrium concepts, and they’re analyzing them as if people will be at equilibrium, but there isn’t always a satisfying explanation of why people will be at Nash equilibrium as opposed to just groping around for one.” If people play a game only once, it is often unreasonable to expect them to find an equilibrium.This is especially the case if — as is typical in the real world — each player knows only how much she herself values the game’s different outcomes, and not how much her fellow players do.

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