Game Theory and Rock, Paper, Scissors
Most children become familiar with the game Rock, Paper, Scissors fairly early on in their lives. For children, this simple game does not require a great deal of thought, as children tend to throw out whichever hand movement they feel like using at the moment. However, the game can be analyzed for optimal strategies. We can create a payoff matrix for the two players, assuming that a win has a value of positive one, a loss has a value of negative one, and a draw has zero payoff. With these assumptions, the matrix looks like this:
Rock Paper Scissors
Rock 0,0 -1,1 1,-1
Paper 1,-1 0,0 -1,1
Scissors -1,1 1,-1 0,0
There is no dominant strategy for either player, no Nash Equilibrium, and no mixed equilibrium. The average expected payoff for each player is zero, so the only strategy for either player is to choose rock, paper, or scissors randomly in hopes that their choice will be the right one. However, one major difference between this game and some others such as the prisoner’s dilemma is that Rock, Paper, Scissors is often played several times in a row for a “best out of five”, or other situation. In those cases, the players can then make decisions about their next play based on the outcome of the previous trial and the other player’s last strategy.
http://nerdist.com/how-to-win-rock-paper-scissors-with-game-theory/
Based on this article and video from Nerdist, studies have shown that people are most likely to repeat their strategy if they won with it. Similarly, the losing player will likely change their strategy. As a result of this, it is optimal for the loser to switch to the strategy that was not played in the round before, as it will beat the winner in the next round, assuming that the winner keeps his or her strategy. If this happens, it is then best for the winner to switch their strategy as well, to the one the loser played, as it will beat the loser’s new strategy. With repeated trials, it is best to pay attention to the behavior of the other player, as playing strategically can become more and more complicated as one looks deeper into the possible outcomes. In some cases, one player’s strategy can become clear if they continue to repeat this strategy, such as choosing the other player’s previous choice. Another strategy to take note of which may be unexpected considering the outcome of the study is to repeat one choice several times in a row. If a player does this two, three, or even four times, the other player may not be expecting it, but as the player continues to do this for more trials, their strategy will become evident to the other player, allowing them to take advantage of it and keep winning. Rock, Paper, Scissors, while a seemingly simple game, can be quite complicated, depending on the players.