Answer to Question #258980 in Math for Tasfia

Question

Consider a new card game between 2 players: Darryl (player 1) and Phyllis (player 2)

Darryl is dealt two cards : ♡6 and ♠5. Phyllis is also dealt two cards: ♢3 and ♣9. Now, each of the players will play 1 card both at the same time.

The payoff of Darryl is 1 points if he plays a card of opposite color (red/black) than Phyllis, and otherwise his payoff is 6 points.

The payoff of Phyllis is 9 points if the difference of the already played card numbers is greater than 5, otherwise her payoff is 1 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 Darryl.

Find the Best Responses for Phyllis.

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