1. (32 total points) Consider the Simplied Poker Game that we played in class. In this variation of the game, all of the rules that were given in class are the same. The only (lilies-cum in the game is that there are 3 Queens and 1 King. So here are the rules of this variation of the Simplied Poker Game: Each player \"soles\" one chip. The \"ante\" is an initial bet made by both players. There are 3 Queens and 1 King. The dealer (Player 1) picks one card at random. The dealer looks at this card. Player 1 can choose to Bet another chip or Fold. If Player 1 Folds, Player 2 wins 1 chip. If Player 1 Bets, then Player 2 can choose to Call or Fold. If Player 2 folds, Player 1 wins 1 chip. If Player 2 Calls, Player 1 reveals the card. If it is a King, Player 1 wins 2 chips; if it is a Queen, Player 2 wins 2 chips. a) (16 points) Complete the following payoff matrix of the Normal Form representation of this game. Player 1 chooses the Row, and Player 2 chooses the Column. The payoffs should be the expected value to each player for each strategy combination. The rst number is the expected value to Player 1, and the second number is the expected value to Player 2. (Hint: It might be helpful to draw the game tree, but you do not need to draw the game tree to get full credit.) -== '3\"'F\"\" == -== -== b) (4 points) Which of Player 1's strategies are Dominated Strategies?c) (8 points) After eliminating the Dominant Strategies, calculate the values for the Mixed Strategy Nash Equilibrium of the remaining game. Let p be the probability of Player 1 choosing (Bet, Bet), so (1 -p) is the probability of choosing (Bet, Fold). Also, let q be the probability of Player 2 choosing Call, so (1 -q) is the probability of Player 2 choosing Fold. P= q =d) (4 points) What is the expected value to Player 1 of this game? EV =