Darryl is dealt two cards : ♡4 and ♠10. Angella is also dealt two cards: ♢3 and ♣8. Now, Darryl will play first and Angella will play second (obviously). The payoff of Darryl is 1 points if he plays a card of opposite color (red/black) than Angella, and otherwise his payoff is 3 points.

The payoff of Angella is 10 points if the difference of the already played card numbers is greater than 5, otherwise her payoff is 3 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 Darryl 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]