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.
Even if we start out knowing only our own preferences and we can’t communicate our strategies before the game, it won’t take too many rounds of missed connections and solitary dinners before we thoroughly understand each other’s preferences and, hopefully, find our way to one or the other equilibrium.
But imagine if the dinner plans involved 100 people, each of whom has decided preferences about which others he would like to dine with, and none of whom knows anyone else’s preferences.
In a paper posted online last September, they proved that no method of adapting strategies in response to previous games — no matter how commonsensical, creative or clever — will converge efficiently to even an approximate Nash equilibrium for every possible game.
It’s “a very sweeping negative result,” Roughgarden said.
“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.
Economists often use Nash equilibrium analyses to justify proposed economic reforms, Myerson said.
But the new result says that economists can’t assume that game players will get to a Nash equilibrium, unless they can justify what is special about the particular game in question.
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).
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.