In this article, a large amount of people repeatedly play rock, paper, and scissors against each other and the results are:
“Upon review of the results, Wang did find numbers that backed up the Nash Equilibrium theory [i.e. neither player gains anything from implementing a strategy other than choosing uniformly randomly from his options] coming into play. He also found the above-mentioned pattern: winners were the players who stayed loyal to their strategy and losers were the players who switched. In game theory, this is called “conditional response.” In fact, the conditional strategy proved to be 10 percent more reliable for winning than did the Nash Equilibrium.”
From this, you should definitely be more cautious in using the Nash Equilibrium. Of course, we did find the Nash Equilibrium for Rock, Paper, and Scissors but we cannot say that will be the best strategy. In fact, often times it’s not (as we have found out in class). Thus, as shown in class and here, we can find the Nash Equilibrium in cases where there are more than two choices but we also need to be careful when applying it – even if it’s a game as simple as Rock, Paper, and Scissors.