"The game of rock-paper-scissors exhibits collective cyclic motions which cannot be understood by the Nash equilibrium concept."<p>This is complete bullshit. It is well understood that if your opponent is not playing an optimum strategy, you can gain an advantage by shifting away from the Nash equillibrium yourself.<p>Example: Image a player that always picks "Paper". By shifting away from a random choice (Nash optimum) to just always selecting "Scissors" will net you a 100% win rate.<p>This is a common trick utilized in poker, where good players will apply a certain playing style, while placing smaller bets, let their opponent adjust to your style and then suddenly change to a more aggressive style. You can take advantage of the fact that your opponent is trying to capitalize on your previous strategy. He has now introduced a sub-optimal element into his game, which you in turn can capitalize on.<p>As in the previous example, imagine we wager $1 on rock paper scissors. I pick paper for the first 100 rounds, you always pick scissors and you always win. Now we suddenly change the bet to one million dollars a hand. I change my selection to "Rock", while you play scissors, as that has given you a perfect win rate so far, and I win the money.