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Positive Affine Transformations (25 points) Consider the following game: Left Right S -3, -3 3, -1 Down -2,5 0,0 a. Find the game's Nash equilibria. b. Now transform all of player 1's utilities by a1(x) + B1, where x is player 1's utility, a1 > 0, and B1 E R. Also transform all of player 2's utilities by a2(y) + B2, where y is player 2's utility, a2 > 0, and B2 E R. Note that you choose the new alpha a and beta B values according to the rules given, and the alpha and beta values may or may not be equal to each other. Write the new game matrix. c. Find the new game's Nash equilibria. d. How do your answers to (a) and (c) compare? e. Choose a new transformation for player 1's payoffs. (It must not be a positive affine transformation.) Explicitly write down that transformation equation. Choose a second transformation and do the same for player 2's payoffs. Then write the new game matrix. f. Find the new game's Nash equilibria. g. How do your answers to (a) and (f) compare? Given that I have no control over what transformation you chose but asked this question anyway, what might this imply about positive affine transformations? This is called a positive affine transformation. You may remember its general construction as "slope-intercept form" from introductory algebra, which looked like y = mx + b. It is "positive" because a; > 0. Note: x and y are the values already in the matrix, and you choose specific values for a and B. Thus a1 (x) + 31 (for every x value in the matrix) and a2 (y) + 32 (for every y value in the matrix) will give you the new payoff values for the new matrix