This question is from " Networks, Crowds, and Markets: Reasoning about a Highly Connected World" textbook in chapter 6

Consider the following statement: In a Nash equilibrium of a two-player game each player is playing an optimal strategy, so the two players strategies are social-welfare maximizing. Is this statement correct or incorrect? If you think it is correct, give a brief (1-3 sentence) explanation for why. If you think it is incorrect, give an example of a game discussed in Chapter 6 that shows it to be incorrect (you do not need to spell out all the details of the game, provided you make it clear what you are referring to), together with a brief (1-3 sentence) explanation.