# Bored with Stripped-Down Poker, Felix and Oscar now make the game more interesting by adding a third

Bored with Stripped-Down Poker, Felix and Oscar now make

the game more interesting by adding a third card type: Jack. Four Jacks are

added to the deck of four Kings and four Queens. 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 the 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 a pooling equilibrium, a

separating equilibrium, or a semi separating equilibrium? (g) In equilibrium,

what is the expected payoff to Felix of playing this game? Is it a fair game?