Please help me with this problem:

Exercise 2:

Felix and Oscar are playing a simplified version of poker. Both make an initial bet of $1. Felix (and only Felix) draws one card, which is either a king or a queen with equal probability (there are four kings and four queens). Felix then chooses whether to Fold or to Bet. If Felix chooses to Fold, the game ends, and Oscar receives Felix's $1 in addition to his own. If Felix chooses to bet, he puts in an additional $1, and Oscar chooses whether to fold or to call. Is Oscar folds, Felix wins the pot (consisting of Oscar's initial bet of $1 and $2 from Felix). If Oscar calls, he puts in another $1 to match Felix's bet, and Felix's card is revealed. If the Card is a king, Felix wins the pot ($2 from each of them). If it is a queen, Oscar wins the pot.

But to make the game more interesting, they decide to add a third type of card: Jack. Four Jacks are added to the initial deck of four queens and four kings. All rules remain the same as before, except for what happens when Felix bets and Oscar calls. When Felix bets and Oscar calls, Felix wins the pot if he has a king, they tie and each gets his money back if Felix is holding a queen, and Oscar wins the pot if the card is a Jack.

(a)Show this game in extensive form (be careful to label information sets correctly)

(b)How many pure strategies does Felix have in this game? Explain your reasoning.

(c)How many pure strategies does Oscar have in this game? Explain your reasoning.

(d)Represent this game in strategic form. This should be a matrix of expected payoffs for each player, given a pair of strategies.

(e)Find the unique pure-strategy Nash equilibrium of this game.

(f)Would you call this equilibrium a pooling equilibrium, a separating equilibrium, or a semiseparating equilibrium?

(g)In equilibrium, what is the expected payoff to Felix of playing this game? Is it a fair game?