1. Suppose there are two players playing a card game with only two cards in the deck, and Ace and a King. First, the deck is shuffled and one of the two cards is dealt to player 1. That is, nature chooses the card for player 1: being the Ace with probability 2/3 and the King with probability 1/3. Player 2 has previously received a card, which both players had a chance to observe. Hence, the only uninformed player is player 2, who does not know whether his opponent has received a King or an Ace. Player 1 observes his card and then chooses whether to bet (B) or fold (F). If he fold, the game ends, with player 1 obtaining a payoff of -1 and player 2 getting a payoff of 1 (that is, player 1 loses his ante to player 2). If player 1 bets, then player 2 must decide whether to respond by betting or folding. When player 2 makes this decision, she knows that player 1 bets, but she has not observed player I's card. The game ends after player 2's action. If player 2 folds, then the payoffs are 1 for player 1 and -1 for player 2 regardless of player I's hand. If player 2 instead responds by betting, then the payoff depends on player 1's card: if player 1 hold the Ace then they payoff for player 1 is 2 and the payoff for player 2 is -2; if player 1 hold the king then the payoffs are -2 for player 1 and 2 for player 2. (a) (2 points) Represent this game in the extensive form. (b) (2 points) Draw the Bayesian normal-form matrix of this game