Find the optimal strategies, P and Q, for the row and column players, respectively. 28 P= Q= x X -5 -5

Determine the maximin and minimax strategies for the two-person, zero-sum matrix game.   −3 5   6 7 The row player's maximin strategy is to play row  .The column player's minimax strategy is to play column  .

Betting Set up the payoff matrix. When you bet on a racehorse with odds of m-n, you stand to win m dollars for every bet of n dollars if your horse wins; for instance, if the horse you bet is running at 5-2 and wins, you will win $5 for every $2 you bet. (Thus a $2 bet will return $7.) Here are some odds from a race. The favorite at 6-2 was Pleasant Tap (P). The second choice was Thunder Rumble (T) at 7-2, while the third choice was Strike the Gold (S) at 4-1. Suppose that just before the race, there has been frantic betting on Thunder Rumble, with the result that the odds have dropped to 4-5 for that horse. The odds on the other two horses remain unchanged. Assume you are making a $30 bet on one of these horses. The payoffs are your winnings. (If your horse does not win, you lose your entire bet. Of course, it is possible for none (N) of your horses to win.) Winner P T N P You Bet T

For the payoff matrix shown , find the optimal strategy for the row and column player and then find expected payoff P = 4 -3 -2 2

Solve the matrix​ game, indicating optimal strategies P* and Q* for R and​ C, respectively, and the value v of the game.​ (First determine if the game is strictly or nonstrictly​ determined.)   M=   -1      3            9    -27   P* = ______  ​(Type an integer or simplified fraction for each matrix​ element.) Q*= ______  ​(Type an integer or simplified fraction for each matrix​ element.) v= ________ (Simplify your​ answer.)

Study techniques Your mathematics test is tomorrow and will cover the following topics: game theory, linear programming, and matrix algebra. You have decided to do an "all-nighter" and must determine how to allocate your 8 hours of study time among the three topics. If you were to spend the entire 8 hours on any one of these topics (thus using a pure strategy), you feel confident that you would earn a 90% score on that portion of the test but would not do so well on the other topics. You have come up with the following table, where the entries are your expected scores. (The fact that linear programming and matrix algebra are used in game theory is reflected in these numbers.) Test Game Linear Matrix Your Strategies Theory Programming Algebra Game Theory 90 80 60 Linear Programming 50 90 50 Matrix Algebra 70 30 90 You have been told that the test will be weighted as follows: game theory: 25%; linear programming: 50%; matrix algebra: 25%. (a) If you spend 25% of the night on game theory,…

Consider the matrix. -6 3 C = -5 4 What is the value of |C]? |C| = %3D

Consider the matrix. -3 5 %3D -24 |C): What is the value of |C =

please answer in text form and in proper format answer with must explanation , calculation for each part and steps clearly

using matrix. Need only handwritten solution only (not typed one).