Nash equilibrium dating
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 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.
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.
“At this point, we don’t have the slow evolution of humanity that only steers us toward games where it is easy to find an equilibrium,” Nisan said.
“We design new games, and if we suppose we’re going to get an equilibrium, we’re very often going to be wrong.” In real life, people often don’t play games at equilibrium, something that economists are keenly aware of, said Andrew Mc Lennan, an economist at the University of Queensland in Brisbane, Australia.