16 Jul SOLVE ONE OF THEM USING ANY OF THE LINEAR PROGRAMMING SOLUTION METHODS
i dont know whether i still believe u guys or not.u guys giving me so much disappointing happening since two previous work, so even u guys told me to discount a lot, i refuse it.but well, hope u guys can work perfectly this time with good price Document Preview: SIT399 Advanced Topics in Mathematics Assignment Two-Option 1 Due: 11am, Monday, May 30th, 2014 Question 1 Find the values of x for which the following games have a saddle point and solve the game for these cases. 1. The 2-by-2 payoff matrix 2. The 3-by-3 payoff matrix Question 2 Find the expected payoff to each player if Player I uses mixed strategy (0.3, 0.7) and Player II uses mixed strategy (0.2, 0.8), in the two-person zero-sum game with the following payoff matrix. Question 3 This question illustrates the following theorem. If one player of a 2-person zero-sum game employs a fixed strategy, then the opponent has an optimal counter strategy that is pure. In other words, if Player I knows that Player II is using a particular mixed strategy y, then Player I can maximize their expected payoff by using a pure strategy, and vice versa. a. Work out the following. i. Find the expected payoff, E(x,y), to Player I if Player I uses mixed strategy (x1, 1-x1), 0 = x1 = 1, and Player II uses mixed strategy (y1, 1-y1), 0 = y1 = 1, in the 2-person zerosum game with the following payoff matrix. ii. Now, think of y1 is being fixed to y1=0.2, find the value(s) of x1 that maximizes E(x,y) for fixed y1. Make your case that, in general, if Player I can use a pure strategy to get the maximum expected payoff, given that Player I knows Player IIs strategy. b. Suppose that Player I knew that Player II is to use a mixed strategy (0.2, 0.3, 0.5) in the game with the following payoff matrix. Work out the three expected payoffs if Player I uses a pure strategy and hence deduce the best strategy for Player I. Question 4 Using the graphical method to solve the 2-person zero-sum game given in Question 2. Question 5 Using the same game given in Question 3(b): 1. Write down the linear programming problems induced by the game. 2. Solve one of them using any of the linear programming solution methods you have learnt so far to find the optimal strategies for both of the players and find the… Attachments: 2014-Assignme….pdf
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