Rock-Paper-Scissors and Game Theory
The main objective of this article is to provide a new perspective on the game of “Rock-Paper-Scissors.” Essentially, Patrick Honner talks about how a short game of “Rock-Paper-Scissors” can instantly turn into a never-ending cycle in which no player ever gets the upper hand for a significant amount of time. Due to the fact that there are no pure Nash equilibria for this game, all of the possible Nash equilibria come from mixed strategies. Person X cannot simply say, “I’m just going to choose rock every time” without expecting Person B to eventually catch on and counter person X’s dominant strategy. Essentially, this would indicate that, when playing “Rock-Paper-Scissors”, there is no better strategy than randomly choosing between the three strategies (as sticking with a fixed strategy ends up costing you in the long run).
The reason I chose to talk about this article was both due to its relation to the notion of mixed strategies (which we have recently just learned about) and because on the shift on perspective that it provides to such an ordinary game loved by our society. Moreover, I wanted to show everyone how this whole notion of finally reaching a certain equilibrium point gets completely demolished when there is no finite number of rounds set. Rather than converge at a certain point, both players just continue to adapt to each other’s erratic change in behavior/strategy. The article goes even further in the sense that it claims that, assuming neither player was aware of each other’s preferences, there would be no guarantee that even a mixed Nash equilibrium point could be reached. Having learned about game theory for the past three to four years, the fact that there could possibly no convergence point shocks me. However, it shouldn’t shock me that much as players don’t have access to those certain pieces of information during a real-world game of “Rock-Paper-Scissors’.” This just goes to show that the notion in which all players involved in games are perfectly rational and know about your preferences is truly idealistic and “perfect.” If not for the unrealistic assumptions, however, then the games shown in lecture would not be possible to complete.
Article: https://www.quantamagazine.org/the-game-theory-math-behind-rock-paper-scissors-20180402/