(a) Consider the following dynamic game between Dante (Player 1) and Beatrice (Player 2). Dante and Beatrice would like to go on a date. They have two options: a movie downtown at Cinemapolis, or a walk along Cayuga lake. Dante first chooses where to go, and knowing where Dante went Beatrice also decide where to go. Dante prefers the movie, and Beatrice prefers the lake. A player gets 3 out his/her preferred date, 1 out of his/her unpreferred date, and 0 if they end up at different places. Use a tree to represent this dynamic game. Find a subgame-perfect Nash equilib rium. Find also a non-subgame-perfect Nash equilibrium with a different outcome, that is, where Dante and Beatrice go on a date in a different place. (b) Modify the game a little bit: Beatrice does not automatically know where Dante went, but she can learn without any cost. That is, now, without knowing where Dante went, Beatrice first chooses between Learn and Not-Learn; if she chooses Learn, then she knows where Dante went and then decides where to go; otherwise she chooses where to go without learning where Dante went. The payoffs depend only on where each player goes, as before. Use a tree to represent this dynamic game. Find a subgame-perfect equilibrium of this new game in which the outcome is the same as the outcome of the non-subgame- perfect equilibrium in part (a). (That is, for each player, he/she goes to same place in these two equilibria.)