Uncertainty and information

S9. Felix and Oscar are playing another simplified version of poker called Stripped-Down Poker. Both make an initial bet of one dollar. 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 dollar in addition to his own. If Felix chooses to Bet, he puts in an additional dollar, and Oscar chooses whether to Fold or to Call. If Oscar Folds, Felix wins the pot (consisting of Oscar's initial bet of one dollar and two dollars from Felix). If Oscar Calls, he puts in another dollar to match Felix's bet, and Felix's card is revealed. If the card is a King, Felix wins the pot (two dollars from each of the roommates). If it is a Queen, Oscar wins the pot. (a) Show the game in extensive form. (Be careful about information sets.) (b) How many strategies does each player have? (c) Show the game in strategic form, where the payoffs in each cell re- flect the expected payoffs given each player's respective strategy. (d) Eliminate dominated strategies, if any. Find the equilibrium in mixed strategies. What is the expected payoff to Felix in equilibrium? S9. Felix and Oscar are playing another simplified version of poker called Stripped-Down Poker. Both make an initial bet of one dollar. 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 dollar in addition to his own. If Felix chooses to Bet, he puts in an additional dollar, and Oscar chooses whether to Fold or to Call. If Oscar Folds, Felix wins the pot (consisting of Oscar's initial bet of one dollar and two dollars from Felix). If Oscar Calls, he puts in another dollar to match Felix's bet, and Felix's card is revealed. If the card is a King, Felix wins the pot (two dollars from each of the roommates). If it is a Queen, Oscar wins the pot. (a) Show the game in extensive form. (Be careful about information sets.) (b) How many strategies does each player have? (c) Show the game in strategic form, where the payoffs in each cell re- flect the expected payoffs given each player's respective strategy. (d) Eliminate dominated strategies, if any. Find the equilibrium in mixed strategies. What is the expected payoff to Felix in equilibrium