Reference no: EM132422764

Problem: Consider a Bargaining Game, which operates as follows. There are two players, Edwin and Xinzhu. There are 3 one-dollar bills on the table. The game proceeds in two stages:

• First, Edwin makes an offer to Xinzhu. The possible offers are (e, 3 - e), where the possible values of e are 0, 1, 2, or 3. The meaning of an offer is that Edwin is proposing that he should get e dollars and Xinzhu should get 3 - e dollars.
• Second, Xinzhu responds to the offer by saying either "Yes" or "No". If Xinzhu says "Yes", then Edwin's offer is implemented and the game ends. If Xinzhu says "No", then the game ends, the money disappears, and both players get nothing.

Assume that each player's utility is equal to the number of dollars he or she has at the end of the game.

Question 1: Draw the game tree for this Bargaining game.

Question 2: The subgame after Edwin has offered (2,1) is a static game with one player, Xinzhu, and two possible actions, "Yes" and "No". Which of these actions are Nash equilibrium actions for Xinzhu in this subgame?

Question 3: The subgame after Edwin has offered (3,0) is also a static game with one player, Xinzhu, and two possible actions, "Yes" and "No". Which of these actions are Nash equilibrium 1 actions for Xinzhu in this subgame?

Question 4: This game has two (pure) Subgame Perfect Nash Equilibria. Find both of them.

Question 5: Is there any Nash equilibrium of this game which is not Subgame Perfect? If yes, list all of them. If no, then explain why.