## Nash Equilibria in Rock-Paper-Scissors

https://www.quantamagazine.org/the-game-theory-math-behind-rock-paper-scissors-20180402/

This article explores the concept of Nash equilibria through a discussion of the game “Rock-Paper-Scissors.” The author explains how if one were to play rock-paper-scissors over and over again instead of stopping after, for example, “best of three,” a point is reached where neither side seems able to improve. This is because, as proved by John Nash, “in any kind of game with a finite number of players and a finite number of optionsâ€”like Rock-Paper-Scissorsâ€”a mix of strategies always exists where no single player can do any better by changing their own strategy alone.” After modeling a situation where two players play the game over and over in order to show how a Nash equilibrium in Rock-Paper-Scissors is reached and what it looks like, the author delves into a discussion as to whether or not, in real life, it is reasonable to assume that players in these kinds of games will naturally arrive at a Nash equilibrium. He notes how with rock-paper-scissors, everyone knows how much everyone else wins and loses for each outcome, it is easier for the equilibrium to be reached. In many cases, however, preferences are secret and more complex, meaning it would take a long time for players to figure out each others strategies and therefore to determine the right strategy to use themselves. He explains that there is “no uniform approach that, in all games, would lead players to even an approximate Nash equilibrium,” so we have no reason to believe that even in a game being played by perfect players, equilibrium will be reached.

In class a large part of our discussion of game theory has revolved around the concept of Nash equilibria. This article illustrates the concept very thoroughly, using a simple game familiar to the large majority of people thus making it easier to understand. It was interesting to see the progression towards a Nash equilibria in the simulation of a game as we haven’t talked about how it is reached in class, only what it is once it has already been reached. Additionally, I liked that the author mentioned that while in rock-paper-scissors all player preferences are known, there are many games in which this is not the case, complicating the process of reaching a Nash equilibrium. I also appreciated the acknowledgement that even when perfect players are playing, there is no guarantee that Nash equilibria will be reached.