Why You Can’t Always Win Rock Paper Scissors
https://www.wired.com/story/why-winning-in-rock-paper-scissors-isnt-everything/
My friend and I can never decide where to eat, because we’re incredibly indecisive, so we decided to play Rock, Paper, Scissors to decide who has to pick where to eat. Silly, I know, but there’s a twist: the loser has to pick which dining hall we go to, and a player has to have a 2 point lead to win. But, this can often take a while when we keep picking the same things.
This article discusses why a Nash equilibrium can be achieved when playing Rock, Paper, Scissors, no matter what strategy the players choose. For example, when the strategies are Player A (¼,½,¼) (rock, paper, scissors) and Player B (½,¼,¼), Player A will win on average 1/16 of a point per round, when winning has a payoff of 1, a tie has a payoff of 0, and losing has a payoff of -1. But, Player B would not want Player A to win, so he could change his strategy by studying Player A’s choices. By doing so, the players would eventually reach the Nash equilibrium, Player A (⅓,⅓,⅓) and Player B (⅓,⅓,⅓), which results in an average of 0 points per player each round. However, it is important to note that just because the payoff of the strategy is an average of 0 points per round, this does that mean that this is a Nash equilibrium. For example, if Player A’s strategy is (⅓,⅓,⅓) and Player B’s strategy is (½,¼,¼), there is a draw, with the players earning an average of 0 points per round, but this is not a Nash equilibrium because Player A could change their strategy to (¼,½,¼) to increase their points average, as explained above.
In class, we learned that when there are no pure strategy equilibria, players will develop a mixed strategy equilibrium, where they will not change their strategies because they can not do better by changing their own strategy if the other players do not change theirs. This article also includes how in Rock, Paper, Scissors, the players can adapt their strategies by studying each other’s moves; if one player does change their strategy, the other can change their probabilities of picking each item, until they reach the Nash equilibrium (⅓,⅓,⅓,), where the average number of points a player earns per round is 0, creating a draw. So, is Rock, Paper, Scissors really the best way to choose who picks dinner? Probably not, because we will reach a Nash equilibrium where it becomes increasingly hard to have a 2 point lead. We should probably just start flipping a coin.