## Game Theory: Rock-Paper-Scissors

Rock-Paper-Scissors is a game that everybody knows how to play, and often a game used to make a decision “randomly”. But the real question is, is the game Rock-Paper-Scissors really that random? Well, in theory, the game has 3 outcomes: a win, loss, or tie. Rock defeats scissors, scissors defeats paper, and paper defeats rock. Players who play Rock-Paper-Scissors have an equal probability of winning, assuming that both players choose options completely randomly. Unfortunately, this is not the case. Rock-paper-scissors actually may not be the most accurate way of deciding something truly randomly. Chinese mathematician Zhijian Wang conducted an experiment involving 72 students to play 300 rounds of rock-paper-scissors. What he discovered was that the student’s decisions during the game tended towards the Nash Equilibrium, which would be picking rock 1/3 of the time, scissors 1/3 of the time, and paper 1/3 of the time. However, despite the Nash Equilibrium, he noticed a pattern with how the games were played. Winners tended to stick with their same strategy, and losers would move on to another strategy. This would repeat for every time a player lost, which he calls “persistent cyclic flows”.

In class, we discussed the “best option” for certain scenarios.  In Rock-Paper-Scissors, there seems to be no theoretical best option, at least mathematically. Each option; rock, paper, or scissors, has an equal probability to win. However, human tendencies make game theory sort of unreliable. Winners think that the option that they won with will win them the game again, and losers think that their option is worse, therefore changing their strategy. In game theory, this is called a “conditional response”. When mathematically modeling rock-paper-scissors, variables such as human tendencies are not factored into deciding which option is the best for each player. Zhijian Wang theorizes that if a player incorporates the knowledge of conditional responses, then he or she may win a lot more often in rock-paper-scissors.