Rock Paper Scissors – How Social Networks Can Affects Mixed Strategies
It’s almost impossible to grow up in the United States without, at some point or another, playing the game “Rock Paper Scissors”. Its simplicity and elegance is matched only by its ubiquity on the playground. This children’s game proves to be a great window into game theory, as a game with no pure Nash equilibrium. Is it possible that this simple game not only has ties to game theory – but also to social networks?
Ever since coming to Cornell from California I have been intrigued by an interesting phenomenon: people from different areas of the world play Rock Paper Scissors differently! I grew up with the following rules: say “Rock – Paper – Scissors” and display your choice (or “throw” as I discovered it is called in RPS circles) on the word “Scissors” – the third beat of the pattern. After coming to Cornell, I learned that many people who grew up in the Northeastern US actually play with a set of slightly different rules: say “Rock – Paper – Scissors – Shoot” and throw on “Shoot”. I began a quest to discover the localities of different rules – for example, a Swiss friend of mine grew up saying “Rock – Paper – Scissors … One – Two – Three” and throwing on “Three”, and many people who went to school in New York City say “Rock – Paper – Scissors – Says – Shoot” and throw on “Shoot”.
My questioning led me to discover a link between the way people play this game and where they grew up. Rock Paper Scissors is a learned game – elementary school teachers teach it as a method of conflict resolution and children spread it throughout their friend groups. As we grow up and our social networks change, however, we encounter people who play in different ways and it can even make us uncomfortable to play this game (that we grew up knowing a specific set of rules for) in a different way.
But how does this have anything to do with game theory? There have been many papers and academic articles that suggest that there is a strategy for Rock Paper Scissors that is statistically superior to others. These strategies are developed by using human tendencies to determine the probabilities for mixed strategies. Take for example, the set of rules that I grew up with, where both players throw on “Scissors”. I discovered that, with this rule set, a significant amount of the time people will throw scissors as their first move. This is because they are thinking and saying the word “scissors”, and this nudges them towards playing scissors. Of course this isn’t guaranteed, but the likelihood of someone throwing scissors is greater than 1/3 (the probability of a random selection). Thus, the best strategy when playing with this set of rules is to throw rock first.
This article from Vice (http://motherboard.vice.com/read/game-theory-rock-paper-scissors) claims that the way to win at Rock Paper Scissors is to understand that people tend to throw the same thing if they won with it the last match and change in a cyclical fashion if they lost. This strategy is only pertinent, however, to game rules where players throw after scissors. The way to win is to predict the probabilities behind the other player’s mixed strategy and determine a strategy based off of that.
What results from these two seemingly distinct analyses, is that the mixed strategies for any given Rock Paper Scissors game depends on the where the players grew up and who they interacted with as children – a pretty cool connection between game theory and social networks.
Dude I’m a Cornell student from California too, and when I noticed this I was so uncomfortable. When I decided to google it just to see if anyone else had noticed before, your blog came up! Great post!
In Rochester, NY, in the 1970s and 80s, we said “one straw straw shoot” and threw on “shoot.” I don’t know why we did it this way. I assumed everyone said it until five minutes ago when a friend asked about the origin or meaning of the phrase.
My family just had a whole conversation about this!
I’m also from Rochester and my Michigan husband had not idea about the 1 straw, straw, shoot!