Mario and Tessa have been already going out for dinner for a few weeks. In Mario's view, it is already time that they start something serious, and he is contemplating to propose (P) her to become his fiance. Tessa has to accept (A) or reject (R). If she accepts, he wants to take her to Italy during Christmas to introduce her to his parents and grandparents. But he fears she may say no, in which case he will suffer a big self-confidence hit. Given this, he may simply choose not to ask her (N). Tessa's dilemma is that she is not sure if Mario is a faithful (F) or an unfaithful (U) guy. (She has read plenty of news about the adventures of II Cavaliere Silvio Berlusconi ((-;) and she thinks there is a chance Mario is one of this kind of men.) While Mario knows himself, she has just got the impression that these types are equally probable. The game-tree representation is as follows: The variable 1 is meant to be Tessa's posterior belief that she will be dating a faithful guy. 1. Derive the perfect Bayesian pure strategy separating equilibria of the game. [Type your answers with the necessary explanations.] 2. Derive the perfect Bayesian pure strategy pooling equilibria of the game. [Type your answers with the necessary explanations.].