Can you guarantee that the Nash Equilibrium will be achieved?
In class, we learned about the concept of the Nash Equilibrium which is the state when all the players in the game don’t have the incentive to change their strategies. Whether it results in pure or mixed strategy, there exist mutual best responses among players. One of the articles from Quanta Magazine, however, asserts something different. Erica Klarreich, the contributor of the article “In Game Theory, No Clear Path to Equilibrium,” applies the Game Theory to the real world and claims that it cannot be assumed that players will eventually achieve the state of the Nash Equilibrium especially with the large pool of players.
Until now, I have never thought of this aspect since I was solely concentrated on solving the problems. But, after I read this article, I started to perceive the Game Theory from the position of actual players of the game. The assumption that I need to take into account is that players are only aware of their own payoffs. Accordingly, it is almost impossible for players to identify the Nash Equilibrium after the first round of the game. As the round proceeds further, people will gradually acquire data of others’ preferences and hopefully get closer to the Nash Equilibrium, but we cannot be certain that the players will reach the exact Nash Equilibrium in the end. Given that we, as solvers of the problem, know each player’s payoffs, the Nash Equilibrium could be recognized, but we cannot guarantee that the actual players will be able to attain that equilibrium.
Instead, Erica explains an alternative concept called the Correlated Equilibrium. In order for the Correlated Equilibrium to be accomplished, the role of the trusted mediator is significant. Advice should be reliable so that the players would not deviate from the suggested strategy. After I acknowledged this new term, it reminded me of the Prisoner’s Dilemma. If we assume that two possible suspects know that they are given an identical condition, the suspects can actually construct the payoffs matrix and find the equilibrium in which both are better off. In this context, the prosecutor is similar to the mediator in the sense that he or she helped the suspects in making decisions. I think the Correlated Equilibrium is more applicable to the real world and it was surprising to know that the Nash Equilibrium was introduced to the world before the Correlated Equilibrium.
https://www.quantamagazine.org/in-game-theory-no-clear-path-to-equilibrium-20170718/