Is Scissors the Dominant Strategy for Rock, Paper, Scissors?
The Japanese electronics giant Maspro Denkoh Corporation Network decided to auction off its $20 million art collection, including the famous Landscape by Paul Cezanne “Les grands arbes au Jas de Bouffan” and works by Pablo Picasso, Vincent van Gogh, and others. The company president Takashi Hashiyama was indifferent to consigning the auction to Sotheby’s of Christie’s (both auction houses in the US). Therefore, he decided to put the decision in the hands of a game of rock, paper, scissors.
Sotheby’s representative, just like most people, thought it was all up to chance, since there’s basically a 1/3 chance of either player choosing to pick rock, paper, or scissor. However, Christie’s representative consulted multiple parties, and figured out the “dominant strategy” to “always play scissors.” Based on game theory we learned in class, how to find the dominant strategy, whether there is one, and drawing payoff matrix, can we confirm that choosing scissors is the dominant strategy?
Here’s a payoff matrix for 2 players playing the game with 1/3 chance of picking each of the choices.
There is no pure strategy, since the payoff for any choice such as Blue player choosing Rock is simply: 
If both players constantly employ this strategy, the payoff would consistently tie at 0.
But is there a mixed strategy in response to this lack of pure strategy?
If Red player were to switch to an imbalanced strategy, where one option, say Rock, Red player would simply alter their strategy to play Paper more frequently. This result would ultimately result in a positive net payoff for Blue Player.
In math terms, based on the payoff (Rock, Paper, Scissors), Red player changes his choice probability to (1/2 Rock, 1/4Paper, 1/4 Scissors). In turn, Blue player changes his choice in response to the new strategy with more Rock (1/4Rock, 1/2Paper, 1/4 Scissors). The payoff would look like this:
This proves, that there exists a mixed strategy that would result in a nash equilibrium. But there’s no proof that Scissors is necessarily the dominant strategy, since like in this example, the opponent could just change their strategy to get a positive payoff.
Cohen, Alina. “How a game of rock, paper, scissors decided a $20 million auction consignment”. Cnn 2019. https://www.cnn.com/style/article/artsy-christies-sothebys-rock-paper-scissors/index.html