Game Theory, Psychology, and Cartoons
Over the weekend I was having a bowl of cereal while watching one of my favorite shows, Regular Show. In this episode Mordecai and Rigby, the two main characters, decided to play a game of Quartz Parchment Sheers or in other word Rock Paper Scissors (RPS). This game was to decide who would get to keep an amazing chair that they found. At first Mordecai wanted to play “Punchies” for it which is a game where the person who punches their opponent the hardest wins. Rigby, being the smaller of the two, was fed up with always losing “Punchies”, so he wanted to play “a game with a little more skill”. RPS is a classic game that is usually not given much thought. A game of practically pure luck. But what if this wasn’t the case? What if Rigby, the cartoon racoon from a kids show, had a point? This got me thinking about psychological thought process that goes behind Rock Paper Scissors and how it could be applied to game theory.
According to a study conducted by Zhejiang Gongshang University, there is a psychological pattern when you play Rock Paper Scissors that will allow you to have a higher chance of winning. In a typical game of RPS there is no dominant strategy that can be utilized. In RPS you and your opponent only have three options to choose from. In a controlled setting you should have fundamentally a 1/3 chance of winning. The game theory graph for RPS looks like this:
| Rock (1/3) | Paper (1/3) | Scissors (1/3) | |
| Rock (1/3) | 0, 0 | -1, 1 | 1, -1 |
| Paper (1/3) | 1, -1 | 0, 0 | -1, 1 |
| Scissors (1/3) | -1 ,1 | 1, -1 | 0, 0 |
Here it is shown that there is no pure strategy Nash equilibrium for RPS. However, there is a way to change those odds. In this study, 360 students were observed and were split up into 6 groups of 60. Within these 6 groups they played amongst themselves. What researchers observed was that the students generally tended to employ a win-stay lose-shift strategy. This means that those who won their game of RPS were more likely to play the same action next time and those who lost are more likely to change to the action they have just been beaten by. There should be no incentive in a game theory version of RPS to change your action because it will have the same probability of winning however, when you factor in human behavior the ideal actions change.
To improve an individual’s chances of winning, when considering human behavior, there is a clear methodical strategy to follow. For example, if you just won a game with Rock on the next round you should switch to Paper which is the action that would’ve beaten you. Also, if you just lost your previous game with Rock you should switch to Scissors which is the action that beats what your opponent just played. This will give an individual the highest likelihood of winning a game of RPS. This shows how there is a cyclical process in RPS that isn’t exactly given recognition in a regular game theory graph. This allows there to be a dominant strategy since you now have a higher chance of winning employing this method given certain circumstances.
Sources:
Quintel, J. G. (2011, July 11). First Day. Regular Show. episode, Cartoon Network.
Article:
Scientists find a winning strategy for rock-paper-scissors | Ars Technica