In class, we played a simplified version of poker, played by the professor against a student. We each ante, then

I draw a card, then I bet or fold, and if I bet, you either call or fold. If I fold, you win my $1 ante. If you fold, I

win your $1 ante. If I bet and you call, I win $2 from you ($1 ante plus $1 additional bet) if I have a king, and

lose $2 to you if I have a queen. We computed the equilibrium to that game in class.

Now let's consider a slightly more complicated version of that game. Suppose that I now use a deck with three

types of cards: 4 kings, 4 queens, and 4 jacks. All rules remain the same as before, except for what happens

when I bet and you call. When I bet and you call, I win $2 from you if I have a king, we "tie" and each get back

our money if I have a queen, and I lose $2 to you if I have a jack.

a. Draw the game tree for this game. Label the two players as "professor" and "student." Be careful to label

information sets correctly. Indicate the payoffs at each terminal node.

b. How many pure strategies does the professor have in this game? Explain your reasoning.

c. How many pure strategies does the student 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 to this game. Explain in English what the strategies are.

f. Would you call this a pooling equilibrium, a separating equilibrium, or a semi-separating equilibrium?

g. In equilibrium, what is the expected payoff to the professor of playing this game?