Question

Dwight is dealt two cards : ♡4 and ♠3 . Angella is also dealt two cards: ♢7 and ♣2 . Now, Dwight will play first and Angella will play second (obviously). The payoff of Dwight is 6 points if he plays a card of opposite color (red/black) than Angella, and otherwise his payoff is 4 points. The payoff of Angella is 1 points if the difference of the already played card numbers is greater than 4, otherwise her payoff is 6 points. Build up the game tree for this extensive form game. Mark the decision nodes as h1 , h2 , etc. and find N , A , H , Z , ρ and χ . [10] Convert the given extensive form game into an induced normal form. [6] Is it possible for Dwight to play a card which will be always better than playing the other card? Write your own opinion.[7] Is it possible for Angella to play a card which will be always better than playing the other card? Write your own opinion. [7]

Answer 1

Answer:

Consider a new card game between 2 players: Dwight (player 1) and Angella (player 2)

Dwight is dealt two cards : ♡4 and ♠3. Angella is also dealt two cards: ♢7 and ♣2. Now, each of the players will play 1 card both at the same time.

The payoff of Dwight is 6 points if he plays a card of opposite color (red/black) than Angella, and otherwise his payoff is 4 points.

The payoff of Angella is 1 points if the difference of the already played card numbers is greater than 4, otherwise her payoff is 6 points.

Find the action sets of each player and the action profile of the game.

Represent the game in the Normal form.

Find the Best Responses for Dwight.

Find the Best Responses for Angella.

Find all the Nash Equilibriums of the game (if any).