Take Quiz B1) Consider the following game table for a simultaneous-move game between A and B: Player B G K O R W G 1, 4. 2 2. 2 5. 1 8. 1 K 2. 2 5, 3 4. 4 2, 2 3. 3 L, O L 5. 3 3. 6 , 6 5, 4 1, 2 2, 2 Player A 2. 3 1. 5 . 2 4, 4 4. 1 1, C R 2. 2 1, 5. 5 3. 3 3, 3 1, 4 W 3, 2 1, 6. 6 0, 1 0. 1 3, 4 a) Iteratively eliminate all dominated strategies in this game. Explain the reason for each elimination and illustrate the game table that emerges after doing so. [6 marks] b) Find all pure-strategy Nash equilibria in the game. Explain how you find them. [2 marks] A couple wants to pick their mobile service providers between Telstra and Optus by Friday. Unfortunately, the wife is on a business trip until Saturday, so they cannot make the decision together. The husband gets to decide first, and the wife decides after she returns. The service of Telstra gives the husband a value of 20, and the service of Optus gives him a value of 22. Just before the husband's decision, Telstra introduced a reward program giving any customer a rebate if a family member joins after the original customer joins. (Note that the rebate can only be received by the family member who joins Telstra first). The rebate adds 5 to the value that the customer places on the service. The service of Telstra always gives the wife the value of 23. The service of Optus gives her a value of 26 if the husband also uses Optus and a value of 25 otherwise. c) Represent the above game using a game tree. [2 marks] d) Find all the subgame perfect Nash equilibria in pure strategies. Explain why they are subgame perfect Nash equilibria. [2 marks] e) Suppose the rebate is x instead of 5. Are there values of x for which both the husband and wife choose Telstra? If yes, find the smallest possible x with this property and explain how you find it; if no, explain why. [2 marks]