4. 2 X Y 1 X 1, 1 0,0 Y 0,0 0,0 Consider the normal form game pictured here: (a) What is the set of rationalizable strategy profiles in this game? 5 points (b) Determine the game's pure strategy Nash equilibrium strategy profile(s). 5 points (c) Does this game have a mixed strategy equilibrium in which both X and Y are played with positive probability? 5 points 5. Consider a game in which, simultaneously, player 1 selects a number x = [0, 20] and player 2 selects a number y [0, 20]. The payoffs are given by: u(x, y) = 2xy - x2 u2(x, y) = 10y+xy - y2. 2 (a) Calculate and graph each player's best-response function, as a function of the opposing player's pure strategy (equivalently, expected strategy). 5 points (b) Determine the rationalizable strategy profiles for this game. Show your logic. 5 points