That's neither my memory of the phrase from school nor my reading of the Wikipedia article. Nash equilibrium may not exist if one of the players follows, say,

That's neither my memory of the phrase from school nor my reading of the Wikipedia article. Nash equilibrium may not exist if one of the players follows, say, a Markov switching process. If that process causes the opponent to stop seeking equilibrium or to settle into a false equilibrium, then the switching process may have been a better strategy than seeking equilibrium.