(Ultimatum with a Finite Number of Alternatives) Players 1 and 2 are bargaining over how to split 10 dollars. Player 1 proposes to take s1 dollars (s1 should be in whole dollars), leaving (10 − s1) dollars for player 2 . Then player 2 either accepts or rejects the offer. If player 2 accepts the offer, the payoffs are s1 to player 1 , and (10 − s1) to player 2. If player 2 rejects the offer, the payoffs are zero to both. (a) Represent this game in extensive form using a game tree. (b) How many pure strategies are there for player 2 in this game? Provide any one strategy for player 2 . (c) Find all the pure-strategy Nash equilibria for the game. (d) Identify those pure-strategy Nash equilibria which are subgame prefect or not. Justify your answers.