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Rock Paper Scissors and Game Theory

https://www.cnn.com/style/article/artsy-christies-sothebys-rock-paper-scissors/index.html

 

The article details how in 2005, two rival auction houses decided to fight between the rights to sell a 20 million dollars worth of art that Japanese electronics company president, Takashi Hashiama owned with a game of rock, paper, scissors. Christie’s was able to beat Soetheby’s: the former played scissors and the latter played paper. Christie’s employed the use of psychology to make the decision. The logic employed was that rock would be too obvious and that the other side would pick paper, so scissors would have the best chance for winning. However, the representative from Soethby’s made their pick randomly. The game is not just a matter of luck, strategy can be applied to yield the best possible chance of winning (scissors). 

This can be proven in this case with a three-by-three payoff matrix that assumes that the dominant strategy is to choose scissors with the aforementioned assumptions. This can be explained with a mixed strategy in that Sotheby’s is operating under a mixed strategy of picking rock less than ⅓ of the time because it is the obvious choice and paper more than ⅓ of the time because it would be used to counter rock. If Sotheby’s pursued a pure strategy then Christie’s would not have a dominant strategy. Because Sotheby’s is most likely to pick paper, then Christie’s dominant strategy would have to be to pick scissors. Therefore, the Nash Equilibrium is Christie’s winning with a choice of scissors and Sotheby’s losing from picking paper.

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