Consider the following simplified version of poker. There is a deck with three cards: Jack (lowest), Queen, King (highest). The game starts with each player receiving a card from the deck (they see their own card but not their opponent's and they cannot receive the same card) and putting a single chip in the pot. The first player acts first and can choose from two actions: bet or check. If he bets, the second player can choose fold or call. If instead the first player checks, the second player can bet or check. If the second player bets, the first player can choose call or fold. The result of any action where no additional decision is specified a terminal. Every time a player bets or calls he must add a single chip to the pot. If the terminal is the result of a fold, the player who did not fold gets all the chips in the pot. Otherwise there is a showdown, and the player with the higher card gets all the chips in the pot. Each player's utility is the number of chips won or lost. (a) Information Sets What are the information sets for this game. (Hint: There are 12) (b) Equilibrium Consider the following strategies. Player 1 begins by checking. Player 2 checks with a Jack or Queen and bets with a King. Player 1 then calls with a King and folds with a Jack or Queen. Argue that they do not form a Nash equilibrium. (Hint: Find an information set where one of the players has a better strategy.)