Nash equilibria – benefits and shortcomings
https://www.newyorker.com/news/john-cassidy/the-triumph-and-failure-of-john-nashs-game-theory
This article contemplates the successes and failures of Nash Equilibria in describing phenomena. Game theory had existed prior to John Nash’s research however it only explained outcomes in zero-sum-games such as poker in which one person’s gain is another person’s loss. Nash’s discovery built on this idea of game theory and allowed for situations to be explained that did not have a winner or loser. For example, a set of farmers are dividing up a market. This is not a zero sum game, it is rather dividing up profits, and Nash was able to explain these phenomena as scientists in the past could not accurately.
Nash was able to prove that given a finite number of players and a finite set of moves, there must exist an equilibrium. The article goes on to posit that Nash’s theories had serious drawbacks in usefulness for several reasons. One being that it is only applicable in a setting with a finite number of moves and a finite number of players. Such a situation is not always common in the real world where people will adhere to such strict rulesets and defined actions. Another drawback is that there could be several Nash Equilibria with equal value and no way to determine which equilibria will be selected. This is a drawback of a theory that was designed to pick out particular solutions.
The article suggests that we ought to use Nash Equilibria for what it is good at whilst acknowledging its drawbacks. Nash Equilibria are good at suggesting what will not happen, and we can make decisions from this information. This tactic is used often by legislators when proposing if a new rule would have a desired affect. Such applications of Nash Equilibria are helpful. The article suggests that we acknowledge the flaws of the theories pushed forward by John Nash whilst using his breakthroughs for what they are truly good at.