Game Theory and Nash Equilibrium
https://www.popsci.com/story/technology/game-theory-explained/
In an article titled “It’s time to explain some game theory” published on Popular Science, Rob Verger attempts to fix the misunderstandings of this field of study. Verger begins with a simple example of game theory regarding slices of pie in order to get the reader to begin analyzing the role of this theory in day to day events. In this example Verger states that there are 3 slices of apple pie and four friends are all interested in getting one slice. This example works to portray game theory as the four friends have to be strategic in order to win or in this case get a piece of the apple pie. Verger states various moves one friend could make that would lead to different outcomes. For instance, if one friend decides to grab the first slice they see they risk clashing with another friend going for that same slice. Generalizing this example Verger then quotes William Spaniel’s (political science professor at University of Pittsburg) definition of game theory as “the scientific study of strategic interaction.” Spaniel emphasizes that in game theory one’s actions effects another’s and vice versa. Furthermore, Spaniel focuses on Nash equilibrium in game theory and how it has been interpreted famously and incorrectly in a 2001 film titled “A Beautiful Mind.”
As we learned in class a Nash equilibrium occurs when strategies are best responses to each other. During a bar scene in this 2001 film this definition was incorrectly interpreted. In this scene there are 5 women one with blonde hair and the other 4 with brown hair. The group of men in the video all want the women with blonde hair. In order to achieve a Nash equilibrium one of the men suggest that no of them should go for the women with blonde hair in order to make sure everybody wins. This is in fact false as in a Nash equilibrium all players should not want to change strategies. In this scenario all the men would want to change up their strategies and go for the blonde women after realizing no other “player” went for her. The blonde women in this case is working to push the system toward a different outcome. In order for this to be a true Nash equilibrium one of the men need to go for the blonde women leaving the rest to go for the other women. This will ensure that all the players in this game are doing their best and would not want to switch their strategies. For a Nash equilibrium to occur in a game all players must believe switching their strategies will result in a worst outcome.