**Practice*** Amy and Bob are playing the following board game:(I) Amy starts. She has three possible actions: Pass, Attack, or Defend.(II) Bob observes what Amy chose, and then chooses between three actions with the same names: Pass, Attack, or Defend.(III) If either player passes, or one attacks and the other defends, then the game ends. But if either both players attack, or if both players defend, then Amy has to choose between two actions: Respond or Not Respond. The payoffs are as follows:- If both players pass, both players get a payoff of 0.- If a player attacks and the other player defends, the player that attacks gets a payoff of 1, while the player that defended gets a payoff of 2.- If a player passes but the other player attacks or defends, the player who passes gets a payoff of -1, and the player who attacked or defended gets a payoff of 3.- If both players attack or both players defend:– If Amy responds, she gets a payoff of 4, and Bob gets a payoff of 0.– If Amy does not respond, each player gets a payoff of 1. If only one of the options from (a)-(c) are true, choose that option. Otherwise, choose either (d) or (e).a. There are 6 subgames.b. An example of a strategy for Amy in this game is (Respond).c. The final payoff in a SPNE is (10,0)d. More than one statement above is true.e. None of the statements above are true.
**Practice***
Amy and Bob are playing the following board game:
(I) Amy starts. She has three possible actions: Pass, Attack, or Defend.
(II) Bob observes what Amy chose, and then chooses between three actions with the same names: Pass, Attack, or Defend.
(III) If either player passes, or one attacks and the other defends, then the game ends. But if either both players attack, or if both players defend, then Amy has to choose between two actions: Respond or Not Respond.
The payoffs are as follows:
- If both players pass, both players get a payoff of 0.
- If a player attacks and the other player defends, the player that attacks gets a payoff of 1, while the player that defended gets a payoff of 2.
- If a player passes but the other player attacks or defends, the player who passes gets a payoff of -1, and the player who attacked or defended gets a payoff of 3.
- If both players attack or both players defend:
– If Amy responds, she gets a payoff of 4, and Bob gets a payoff of 0.
– If Amy does not respond, each player gets a payoff of 1.
If only one of the options from (a)-(c) are true, choose that option. Otherwise, choose either (d) or (e).
a. There are 6 subgames.
b. An example of a strategy for Amy in this game is (Respond).
c. The final payoff in a SPNE is (10,0)
d. More than one statement above is true.
e. None of the statements above are true.
Step by step
Solved in 1 steps
