 From this, we see that an evolutionarily stable strategy is a Nash equilibrium with an additional second-order stability criterion. It is a proper strengthening of the Nash equilibrium concept, because whereas every game with finitely many players and a finite number, of strategies has at least one Nash equilibrium (if mixed strategies are allowed), not every game has an evolutionarily stable strategy. It is easily shown that the game of Rock-Scissors-Paper, shown in figure 3, does not have an evolutionarily stable strategy. (The only potential candidate for being evolutionarily stable is the Nash equilibrium mixed strategy \(\sigma\) which assigns equal probability to all three pure strategies. But since \( \pi( \sigma \mid \sigma) = \pi( \text{Rock} \mid \sigma) \) and \(\pi(\sigma \mid \text{Rock}) = \pi( \text{Rock} \mid \text{Rock})\), it is not evolutionarily stable.)