Rock, Paper, Scissors, Game Theory, & Imitation
While many of us think we have the best strategy to win rock-paper-scissors, or roshambo as some would have it, the reality is that the best strategy to winning is to choose randomly. Nevertheless, scientists have made a discovery. In a series of studies blindfolded participants were pitted against each other, and a group of blindfolded versus nonblindfolded participants battled as well. They found that when playing the game, participants unconsciously mimicked the other player. The blindfolded skirmishers had 33.3% chance of drawing (both playing the same move), however, the blind verse enlightened had a 36.3% chance of drawing. Scientists explain this discrepancy as instinctive mirror responses, know as atomatic imitation. During the fraction of seconds after the first player has played a random move, the second player’s choice of move is influenced by the first. This automatic imitation may be due to the “mirror neurons” which have been suspected of controlling mimicry behavior. I believe the contagious yawn phenomenon has been attributed to these neurons as well.
It is interesting that such a phenomenon exists. The game of rock-paper-scissors is a fairly simple game, with 9 outcomes, 3 of which are ties, 3 of which result in wins for player 1, and 3 which result in wins for player 2. The payoff matrix is pretty easy to construct, and its easy to see that there is no pure strategy Nash equilibrium for the game. There is, however, a mixed strategy solution which indicates random selection as the strategy of choice. This illustrates that humans are not capable of applying game theory perfectly. Despite a fairly simple Nash equilibrium strategy, players deviate.
(player1,player2) Rock Paper Scissor
Rock 0,0 -1,1 1,-1
Paper 1,-1 0,0 -1,1
Scissor -1,1 1,-1 0,0
This article illustrates that, although game theory is perfectly accurate, its suggestions about equilibria are not always adhered to by the players. Its interesting that our subconscious can get in the way, particularly in such a silly way as a desire to imitate. The moral of the story is, next time you you are faced with a roshambo challenge, be sure to choose randomly.
http://www.bbc.co.uk/news/science-environment-14199110