Consider the modification of the old card game introduced in assignment 1 between 2 players: Darryl (player 1) and Pam (player 2)
Darryl is dealt two cards: ♡4 and 8. Pam is also dealt two cards: 8 and 9. Now, Darryl will play first and Pam will play second (obviously).
The payoff of Darryl is 2 points if he plays a card of opposite color (red/black) than Pam, and otherwise his payoff is 3 points.
The payoff of Pam is 2 points if the difference of the already played card numbers is smaller than 4, otherwise her payoff is 3 points.
1. Build up the game tree for this extensive form game. Mark the decision nodes as h₁, h₂, etc. and find N, A, H, Z, p and X. [10]
2. Convert the given extensive form game into an induced normal form. [6]
3. Is it possible for Darryl to play a card which will be always better than playing the other card? Write your own opinion. [7]
4. Is it possible for Pam to play a card which will be always better than playing the other card? Write your own opinion. [7]
Answers
Answer:
Transcribed image text: Consider the modification of the old card game introduced in assignment 1 between 2 players: Darryl (player 1) and Pam (player 2) Darryl is dealt two cards : ♡4 and 48. Pam is also dealt two cards: 08 and 49. Now, Darryl will play first and Pam will play second (obviously). The payoff of Darryl is 2 points if he plays a card of opposite color (red/black) than Pam, and otherwise his payoff is 3 points. The payoff of Pam is 2 points if the difference of the already played card numbers is smaller than 4, otherwise her payoff is 3 points. 1. Build up the game tree for this extensive form game. Mark the decision nodes as hi, h2, etc. and find N, A, H, Z, p and X. [10] 2. Convert the given extensive form game into an induced normal form. [6] 3. Is it possible for Darryl to play a card which will be always better than playing the other card? Write your own opinion.[7] 4. Is it possible for Pam to play a card which will be always better than playing the other card? Write your own opinion. [7]