Here is a description of the simplest poker game. There are two players and only two cards in the deck, an Ace and a King. First, the deck is shufed and one of the two cards in 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 folds, 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 betting or folding. When player 2 makes this decision, she knows that player 1 bets, but she has not observed player l's card. The game ends after player 2's action. If player 2 folds, then the payoff vector is (l, -l), meaning player 1 gets 1 and player 2 gets 1, regardless of player 1's hand. If player 2, instead, responds betting, then the payoff depends on player l's card: if player 1 holds the Ace then the payoff vector is (2, -2), thus indicating that player 1 wins; if player 1 holds the King, then the payoff vector is (-2, 2), reecting that player 1 looses. Represent this game in the extensive form and in the Bayesian normal form, and nd the Bayesian Nash Equilibrium (BNE) of the game