There is no dearth of fads in this world, but using the game of Rock Paper Scissors as a strategic decision tool is rich. It seems that it has been used in some key decisions in few scenarios atleast, also its been getting due attention from mass media e.g. this column in the Fortune magazine by Jennifer Crick:
You may ask, "Why not just toss a coin?" The difference is that while coin-tossing relies solely on random odds, RPS, despite what many people think, doesn't. What's fascinating about RPS is that it's a competition to simultaneously read your opponent's mind and prevent him from reading yours. And unlike other games that involve reading and misleading your opponent (like poker), you can't win RPS by bluffing alone. Eventually you have to show your hand.
Winning at RPS is all about knowing what your opponent is going to do. Successful strategizing involves a series of mental questions: "If you know that I know that you know that I know …" The popular name for this strategy is Sicilian Reasoning. Part of the trick is knowing when to stop the series; otherwise you risk overestimating your opponent's intelligence (and outwitting yourself). Another part is knowing where to start: Ask yourself, "Deep down, is my opponent rock, paper, or scissors?"
On the pop culture front, as also mentioned in the same article, there is a world RPS championship. More interesting is the competition between bots as mentioned on the RSBPC page. Sicilian Reasoning, as referenced in the article is just one of the strategies, but is most intriguing of the lot: it goes counter to what we normally do in real life – we over analyze the past patterns and lean in favour of winning moves, the Sicilian Reasoning advises biasing against the past moves. As mentioned in the RSBPC page the small programs do as well as complicated algorithms, there is even a mention of a one-liner implementation called 'Henny'.