Game Theory in Rock Paper Scissors?
https://www.quantamagazine.org/the-game-theory-math-behind-rock-paper-scissors-20180402/
This article describes game theory in the context of the popular game, rock paper scissors. As kids, we’ve all encountered that point in the game where we think we have a successful strategy that we can stick to for the rest of the game and win easily, only to find on the next play that your opponent has predicted your moved. The author starts by posing the play that each player picks one of the 3 possible moves and sticks to it for the rest of the game. Thus, if a pure strategy is picked, the game goes in circles and there is no Nash equilibrium established. The author proposes that the most sensible strategy in this game would be for Player A and Player B to allocate equal probabilities to the 3 possibilities i.e (1/3, 1/3, 1/3) for rock, paper scissors for Player A and Player B. The author calculates the matrix below, based on the payoffs that a win gives 1 point, a loss gives -1 and a draw results in 0 points. The calculation results in a net result of a draw and the game reaches Nash equilibrium.
(from the website)Any other combination probabilities for Player A and Player B would not result in a Nash equilibrium, as the author hashes out in the rest of his calculation. The discussion of pure vs mixed strategy is similar to the discussion in class regarding the football game, where payoffs between the striker and the goalie were calculated to show that a mixed strategy would be the best here. The difference is that, here, the players could pick a move from 3 options compared to 2.
I always wondered why some people are just “better” at rock paper scissors than others- it’s those who don’t know what they’re doing the next move that do well!