Rock Paper Scissors and Game Theory

game theory

The game of Rock-Paper-Scissors, or as Pops from the Regular Show calls it, Quartz-Parchment-Shears, has long puzzled mathematicians. There does not seem to be a sure way to win. However, a recent experiment indicates that there are predictable ways to win the time-honored, important decision-making game. By applying math patterns and game theory, Rock-Paper-Scissors can be consistently won.

Zhijian Wang, a mathematician, conducted the experiments at Zhejiang University in China. Using real people playing the game,Wang was able to identify some interesting strategies. He noted that the players who seemed to consistently win had a tendency to stay loyal to their strategy. Conversely, losers were inclined to switch strategies. The switching took on a “persistent cyclic flow.” Winners seem to pay more attention to how their opponent plays whereas losers pay more attention to the outcome of the game.

One thing is known about Rock-Paper-Scissors: there can be only one of three outcomes. Each choice has one other choice it will beat and one other choice that will beat it. It does not matter what strategy is used to win. However, it appears to be a good bet when a player uses rock 1/3, paper 1/3 and scissors 1/3 of the time. This is what is called a Nash Equilibrium. The connection between game theory and Rock-Paper-Scissors is more in-depth than originally believed.

The Nash Equilibrium concept assumes that a player has no reason to alter their chosen strategy, even after considering the other player’s choices. A player gets no additional gains from changing their strategy. This is also assuming that the opponent does not change their strategy. When Wang found 72 test subjects to play Rock-Paper-Scissors, he found that the Nash Equilibrium may not be the optimum strategy after all. Wang and his fellow researchers made 12 groups with six players each. They were then asked to play 300 rounds of the game that is also called Roshambo.

Upon review of the results, Wang did find numbers that backed up the Nash Equilibrium theory coming into play. He also found the above-mentioned pattern: winners were the players who stayed loyal to their strategy and losers were the players who switched. In game theory, this is called “conditional response.” In fact, the conditional strategy proved to be 10 percent more reliable for winning than did the Nash Equilibrium.

The “stay if you win, shift if you lose” phenomenon is sometimes referred to as Pavlov strategy. Some have pointed to deep psychological underpinnings to these behaviors and Wang and his team are eager to explore them. If these responses are essentially hard-wired in the brain, they want to know why.

In the episode of Regular Show titled “First Day,” the main characters, Rigby and Mordecai, choose to play Rock-Paper-Scissors in order to decide who gets to keep an uncomfortable couch. 100 times in a row they tie, creating a black hole monster. When the characters realize what they have done, they break the tie, sending the monster back from whence it came.

As Wang’s research is proving, the chances of tying 100 times are extremely slim. That hardly matters. His experiment is not only fun but educational. Rock-Paper-Scissors is proving to be a great tool for learning more about the world of game theory.

By Stacy Lamy





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