4. ULTIMATUM GAME (25PTS) Consider a variant of the ultimatum game where players 1 and 2 divide 2 dollars between them. Player 1 rst makes a take-itorleaveit offer to player 2, where she can offer to give player 2 an integer number of dollars (i.e., offer :32 = 0,1,2). Player 2 then chooses whether to accept or reject the offer. If 2 chooses to accept, then the two players' payoffs are (2 $2, 51:2). Otherwise, their payoffs are (0, 0). Answer the following questions. (1) Represent the extensive form of the game by a game tree. (5pts) (2) Write down the strategic form of the game and nd all the pure strategy Nash equilibria. (10pts) (3) Find all the pure strategy subgame perfect equilibria. (10pts)