Existing Outside a Nash Equilibrium
Nash dazzled the world with his breakthrough concept of a Nash equilibrium, a point in a game where neither player would want to switch. This discovery changed the way that scholars approached the games that define everyday life. Nash equilibriums helped understand auctions, commutes, and even dilemmas in prison. What made his work so revolutionary was that his approach of looking at games allowed someone to understand the seemingly mysterious ways that players tend to settle into decisions creating a balance in a game over time. These points of equilibrium are complicated and hard to explain, but Nash hypothesized that these were ultimately the eventual outcome of any game that had them.
Nash’s idea quickly took hold in economics and many more disciplines, but that doesn’t mean that they were ever fully understood. While the fact that these equilibriums exist has become accepted fact, the process in which the players end up finding them is much more of a mystery. Aviad Rubinstein, a PhD candidate from UC Berkley, has applied computer models to create advanced versions of Nash’s games. His work has focused on how these equilibria are found in the real world. An example would be 100 people deciding how to go out to dinner, and who with. In this situation, every person has a preferred dining-partner. In this situation, there are 2^100 possibilities. To put this number in reference, there have only been 2^59 seconds since the Big Bang, as pointed out by Erica Klarreich in her piece for Quanta Magazine.
Even if this restaurant-choosing game were to continue round after round with people reassigning themselves with lessons learned from previous rounds, Rubinstein’s work shows that this situation would not quickly find an equilibrium. Finding the equilibrium would take longer than a human’s lifespan, let alone the Universe’s. Rubinstein’s findings add an important caveat to Nash’s work. While games may have an equilibrium point, a spot where players settle into a choice with no benefit of switching, games may not necessarily ever find this point. This adds importance to understanding the process through which people find the Nash equilibrium, especially when considering larger and larger games.
https://www.quantamagazine.org/in-game-theory-no-clear-path-to-equilibrium-20170718/