Please be aware that this question is from Linear Optimization

Coleen (2, 2) (2, 3) (3, 2) (3, 3 ) (2, 2) 3 4 ( Already domination reduced) Ron (2, 3) -4 5 w -3 5 (3, 2) -3 3 -6 (3, 3) W -5 6 V 922 923 932 933 -1 u O -1 -1 = -0 = -t22 P22 -1 -3 40 P23 -1 -4 3 O W W G H UT W H 0 =-t23 (Using natural variable names. ) P32 -1 5 -3 -6 = -t32 3 -5 -3 0 P33 =-33 -1 -1 0 O O 0 0 = f = 0 = $22 =$23 = 532 - 533 =8 t33 t32 t23 933 -1 523 -1/25 -2/75 1/15 17/15 13/25 - 923 1/5 -1/5 0 1 2/5 = -932 532 522 -4/25 17/75 -1/15 -17 /15 2/25 - 922 (I used computer to solve this) P22 3 /5 -3/5 -1 0 1/5 = -t22 -1 -2/25 -29/75 -8/15 -1/15 1/25 = f = P33 = P32 = P23 =$33 =g Ron wins 4 cents per game on average. Optimal strategies: For Ron (P22, P23, P32, P33) = (0, 15 ' 75 ' 25) ). For Coleen (922, 923, 932, 933) = ( 25' 25, 5, 0).Game 2: Guess the Number: Find the optimal mixed strategies for the following matrix game Ron and Coleen simultaneously writes either the number 2 or 3. Each player also writes a number which they believe the opponents has written down. 0 If neither player guesses right, Ron wins $3 from Coleen. o If both players guess right, Coleen wins $3 from Ron. 0 Otherwise, the player who guesses correctly wins (from the other player) the sum (in $) of the (first) numbers written by two players. Notation: The pair (a, b) denotes a player's choice of writing a and guessing b, for a, b 6 {2,3}